Search Results - Boundary value AND inverse problems for harmonic functions in two dimensions*

Some geometric relations for equipotential curves

Authors: Yajun Zhou

Source: Journal of Differential Equations. 433:113296

Subject Terms: Boundary value and inverse problems for harmonic functions in two dimensions, Mathematics - Differential Geometry, Probability (math.PR), FOS: Physical sciences, Mathematical Physics (math-ph), level sets, 01 natural sciences, Mathematics - Analysis of PDEs, harmonic function, Differential Geometry (math.DG), FOS: Mathematics, 0101 mathematics, Harmonic, subharmonic, superharmonic functions in two dimensions, Mathematical Physics, Mathematics - Probability, Dirichlet problem, Analysis of PDEs (math.AP)

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Access URL: http://arxiv.org/abs/1912.11669
https://zbmath.org/8031083
https://doi.org/10.1016/j.jde.2025.113296

The boundary inverse problem for the Laplace equation in two dimensions

Authors: N D Aparicio Michael Pidcock

Source: Inverse Problems. 12:565-577

Subject Terms: Boundary value and inverse problems for harmonic functions in two dimensions, Inverse problems for PDEs, Cauchy problem for the Laplace equation, Ill-posed problems for PDEs, first kind integral equation, boundary determination, 0101 mathematics, ill-posedness, 01 natural sciences, analytic continuation of complex functions

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Access URL: https://zbmath.org/943193
https://doi.org/10.1088/0266-5611/12/5/003
https://iopscience.iop.org/article/10.1088/0266-5611/12/5/003
http://iopscience.iop.org/article/10.1088/0266-5611/12/5/003/pdf

A Fourier method for the construction of certain extremal solutions of the inverse Dirichlet problem in two dimensions

Authors: Stephen P. Huestis

Source: Inverse Problems. 11:1163-1175

Subject Terms: Boundary value and inverse problems for harmonic functions in two dimensions, Inverse problems for PDEs, Lagrange multipliers, boundary value function, Integral representations, integral operators, integral equations methods in two dimensions, Green's function, 0101 mathematics, representation theorem, truncated Fourier series, 01 natural sciences, inverse Dirichlet problem for Laplace's equation

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Access URL: http://iopscience.iop.org/article/10.1088/0266-5611/11/6/003/pdf
http://iopscience.iop.org/0266-5611/11/6/003/pdf/0266-5611_11_6_003.pdf

Some overdetermined boundary value problems for harmonic functions

Authors: Gérard A. Philippin L. E. Payne

Source: ZAMP Zeitschrift f�r angewandte Mathematik und Physik. 42:864-873

Subject Terms: Boundary value and inverse problems for harmonic functions in two dimensions, overdetermined exterior problem, simply connected plane domain, Stekloff eigenvalue problem, Overdetermined systems of PDEs with constant coefficients, General topics in linear spectral theory for PDEs, 0101 mathematics, 01 natural sciences

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Access URL: https://link.springer.com/article/10.1007/BF00944568
http://ui.adsabs.harvard.edu/abs/1991ZaMP...42..864P/abstract

A hybrid method for inverse boundary value problems in potential theory

Authors: Chapko, R. Kress, Rainer

Contributors: Chapko, R. Kress, Rainer

Source: Journal of Inverse and Ill-Posed Problems. 13:27-40

Subject Terms: Boundary value and inverse problems for harmonic functions in two dimensions, regularization, Inverse problems for PDEs, Numerical methods for inverse problems for boundary value problems involving PDEs, Newton method, Tikhonov regularization, Laplace equation, 0101 mathematics, 01 natural sciences, Dirichlet problem

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Access URL: https://zbmath.org/2152326
https://doi.org/10.1163/1569394053583711
https://www.degruyter.com/view/j/jiip.2005.13.issue-1/1569394053583711/1569394053583711.xml?lang=en
https://www.degruyter.com/view/j/jiip.2005.13.issue-1/1569394053583711/1569394053583711.xml
https://resolver.sub.uni-goettingen.de/purl?gro-2/121435

Application of radial basis meshless methods to direct and inverse biharmonic boundary value problems

Authors: Jichun Li

Source: Communications in Numerical Methods in Engineering. 21:169-182

Subject Terms: Boundary value and inverse problems for harmonic functions in two dimensions, Inverse problems for PDEs, collocation, numerical examples, Numerical methods for inverse problems for boundary value problems involving PDEs, 01 natural sciences, Boundary value problems for higher-order elliptic equations, inverse problem, Biharmonic, polyharmonic functions and equations, Poisson's equation in two dimensions, meshless method, Spectral, collocation and related methods for boundary value problems involving PDEs, 0101 mathematics, radial basis function, biharmonic boundary value problem

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Access URL: https://zbmath.org/2159903
https://doi.org/10.1002/cnm.736
https://www.onlinelibrary.wiley.com/doi/abs/10.1002/cnm.736

Reflection and a mixed boundary value problem concerning analytic functions

Authors: Miroslav Dont Josef Král Eva Dontová

Source: Mathematica Bohemica. 122:317-336

Subject Terms: Boundary value and inverse problems for harmonic functions in two dimensions, integral equations, Fredholm type equation, boundary value problem, 0202 electrical engineering, electronic engineering, information engineering, Boundary value problems in the complex plane, 02 engineering and technology, 0101 mathematics, 01 natural sciences

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Access URL: http://dml.cz/bitstream/handle/10338.dmlcz/126150/MathBohem_122-1997-3_10.pdf
https://eudml.org/doc/248124

A boundary value problem with an involutive shift in the boundary condition

Authors: A. N. Zarubin

Source: Differential Equations. 40:1503-1506

Subject Terms: Boundary value and inverse problems for harmonic functions in two dimensions, harmonic function, existence, 0101 mathematics, Harmonic, subharmonic, superharmonic functions in two dimensions, 01 natural sciences

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Access URL: https://link.springer.com/article/10.1007/s10625-004-0019-8

On the Treatment of a Dirichlet–Neumann Mixed Boundary Value Problem for Harmonic Functions by an Integral Equation Method: On the treatment of a Dirichlet-Neumann mixed boundary value problem for harmonic functions by an integral equation method

Authors: R. Kress R. González

Source: SIAM Journal on Mathematical Analysis. 8:504-517

Subject Terms: Boundary value and inverse problems for harmonic functions in two dimensions, Boundary value problems for second-order elliptic equations, General existence and uniqueness theorems (PDE), 0101 mathematics, 01 natural sciences

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Access URL: https://zbmath.org/3556547
https://doi.org/10.1137/0508038
https://epubs.siam.org/doi/abs/10.1137/0508038

Boundary values versus dilatations of harmonic mappings

Authors: Walter Hengartner Daoud Bshouty

Source: Journal d'Analyse Mathématique. 72:141-164

Subject Terms: Boundary value and inverse problems for harmonic functions in two dimensions, Jordan domain, univalent harmonic mappings, General theory of univalent and multivalent functions of one complex variable, Blaschke product, 0101 mathematics, Harmonic, subharmonic, superharmonic functions in two dimensions, 01 natural sciences

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Access URL: https://zbmath.org/1146577
https://doi.org/10.1007/bf02843157
https://link.springer.com/article/10.1007/BF02843157

A Denseness Theorem with an Application to a Two-Dimensional Inverse Potential Refraction Problem: A denseness theorem with an application to a two-dimensional inverse potential refraction problem

Authors: Bernd Hofmann

Source: SIAM Journal on Mathematical Analysis. 30:896-911

Subject Terms: Boundary value and inverse problems for harmonic functions in two dimensions, Inverse problems for PDEs, parameter identification potential refraction, 0101 mathematics, inverse conductivity problem, 01 natural sciences, domain derivative

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Access URL: https://zbmath.org/1308656
https://doi.org/10.1137/s0036141098336108
https://epubs.siam.org/doi/abs/10.1137/S0036141098336108

ON AN INTEGRAL EQUATION OF SOME BOUNDARY VALUE PROBLEMS FOR HARMONIC FUNCTIONS IN PLANE MULTIPLY CONNECTED DOMAINS WITH NONREGULAR BOUNDARY: On an integral equation of some boundary value problems for harmonic functions in plane multiply connected domains with nonregular boundary

Authors: S E Mikhaĭlov

Source: Mathematics of the USSR-Sbornik. 49:525-536

Subject Terms: Boundary value and inverse problems for harmonic functions in two dimensions, logarithmic potential, cusps, Neumann series, Fredholm radius, angular potential, Fredholm integral equations, 01 natural sciences, integral equations method, oblique derivative, corner points, Integral representations, integral operators, integral equations methods in two dimensions, 0101 mathematics, multiply connected domains, Dirichlet problem

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Access URL: http://ui.adsabs.harvard.edu/abs/1984SbMat..49..525M/abstract
http://people.brunel.ac.uk/~mastssm/Papers/Mikhailov_MatSb1984.pdf

Harmonic functions satisfying a radiation boundary condition

Authors: Green H.S. Bracken A.J. Bass L.

Source: Computers & Mathematics with Applications. 22:23-38

Subject Terms: Boundary value and inverse problems for harmonic functions in two dimensions, smooth convoluted boundary, Biochemistry, molecular biology, diffusion, 2611 Modelling and Simulation, Computational Mathematics, 2604 Applied Mathematics, Computational Theory and Mathematics, Modelling and Simulation, Conformal mappings of special domains, 2605 Computational Mathematics, Boundary value and inverse problems for harmonic functions in higher dimensions, membrane

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Access URL: https://espace.library.uq.edu.au/view/UQ:395922
https://core.ac.uk/display/43401710
https://www.sciencedirect.com/science/article/pii/0898122191900397

Note on a boundary value problem of poisson’s equation: Note on a boundary value problem of Poisson's equation

Authors: Yu Hongquan Feng Chaokeng Hsu Li-zhi

Source: Applied Mathematics-A Journal of Chinese Universities. 10:35-38

Subject Terms: Boundary value and inverse problems for harmonic functions in two dimensions, Poisson's equation, 0202 electrical engineering, electronic engineering, information engineering, Biharmonic, polyharmonic functions and equations, Poisson's equation in two dimensions, 02 engineering and technology, Green's function, 0101 mathematics, similarity analysis, 01 natural sciences, Solutions to PDEs in closed form

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Access URL: https://link.springer.com/content/pdf/10.1007/BF02663891.pdf
https://en.cnki.com.cn/Article_en/CJFDTOTAL-GXYY501.003.htm
https://link.springer.com/article/10.1007/BF02663891

On an inverse logarithmic potential problem for a point mass model using data on restricted boundary

Authors: Takashi Ohe Kohzaburo Ohnaka

Source: Nonlinear Analysis: Theory, Methods & Applications. 30:2209-2214

Subject Terms: Boundary value and inverse problems for harmonic functions in two dimensions, Inverse problems for PDEs, Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type, 0103 physical sciences, Fourier transform, uniqueness question, 0202 electrical engineering, electronic engineering, information engineering, window Fourier transform, 02 engineering and technology, point mass model, 01 natural sciences

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Access URL: https://zbmath.org/1112518
https://doi.org/10.1016/s0362-546x(97)00108-9
https://www.sciencedirect.com/science/article/pii/S0362546X97001089

A mixed boundary value problem for a harmonic function in a half-space

Authors: V.N. Vorob'ev A.B. Efimov

Source: USSR Computational Mathematics and Mathematical Physics. 14:232-236

Subject Terms: Boundary value and inverse problems for harmonic functions in two dimensions, Boundary value problems for second-order elliptic equations, Harmonic, subharmonic, superharmonic functions in two dimensions

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Access URL: https://zbmath.org/3487805
https://doi.org/10.1016/0041-5553(74)90211-0
https://www.sciencedirect.com/science/article/pii/0041555374902110

ELEMENTARY EXACT METHOD FOR SOLVING MIXED BOUNDARY-VALUE PROBLEMS OF POTENTIAL THEORY, WITH APPLICATION TO HALF-PLANE CONTACT AND CRACK PROBLEMS: Elementary exact method for solving mixed boundary value problems of potential theory, with application to half-plane contact and crack problems

Authors: V. I. Fabrikant E. N. Karapetian

Source: The Quarterly Journal of Mechanics and Applied Mathematics. 47:159-174

Subject Terms: Boundary value and inverse problems for harmonic functions in two dimensions, Elastic materials, Fracture and damage, charge-density distribution, Theories of friction (tribology), punch problem, half-plane crack, 02 engineering and technology, integral representation, Contact in solid mechanics, integral equation, 0203 mechanical engineering, Dynamical problems in solid mechanics, 0210 nano-technology

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Access URL: https://academic.oup.com/qjmam/article/47/1/159/1889069

A problem of Baernstein on the equality of the 𝑝\mspace{1𝑚𝑢}-harmonic measure of a set and its closure: A problem of Baernstein on the equality of the \(p\)-harmonic measure of a set and its closure

Authors: Björn, Anders Björn, Jana Shanmugalingam , Nageswari

Source: Proceedings of the American Mathematical Society. 134:509-519

Subject Terms: Boundary value and inverse problems for harmonic functions in two dimensions, Matematik, unit disc, 4. Education, starshaped, Capacity and harmonic measure in the complex plane, Potentials and capacities on other spaces, Dirichlet problem for \(p\)-harmonic functions, Sobolev space, 16. Peace & justice, Lipschitz domain, 01 natural sciences, Ahlfors regular, Sobolev function, Minkowski dimension, 0103 physical sciences, starshaped domain, trace, 0101 mathematics, Sobolev spaces and other spaces of ''smooth' functions, embedding theorems, trace theorems, Boundary value and inverse problems for harmonic functions in higher dimensions, Mathematics, Dirichlet problem, Other generalizations (nonlinear potential theory, etc.)

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Access URL: https://www.ams.org/proc/2006-134-02/S0002-9939-05-08187-6/S0002-9939-05-08187-6.pdf
https://zbmath.org/2227192
https://doi.org/10.1090/s0002-9939-05-08187-6
https://www.jstor.org/stable/4098314
https://ams.org/journals/proc/2006-134-02/S0002-9939-05-08187-6/S0002-9939-05-08187-6.pdf
https://documat.unirioja.es/servlet/articulo?codigo=1463236
https://liu.diva-portal.org/smash/get/diva2:217010/FULLTEXT01.pdf
http://www.diva-portal.org/smash/record.jsf?pid=diva2:217010
https://www.ams.org/journals/proc/2006-134-02/S0002-9939-05-08187-6/home.html
http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-18233

Detecting inclusions with a generalized impedance condition from electrostatic data via sampling

Authors: Isaac Harris

Source: Mathematical Methods in the Applied Sciences. 42:6741-6756

Subject Terms: Boundary value and inverse problems for harmonic functions in two dimensions, Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation, 35J05, 31A25, 78A30, FOS: Physical sciences, Mathematical Physics (math-ph), 01 natural sciences, sampling methods, inverse boundary value problems, Mathematics - Analysis of PDEs, Boundary value problems for second-order elliptic equations, FOS: Mathematics, shape reconstruction, 0101 mathematics, Mathematical Physics, Analysis of PDEs (math.AP)

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Access URL: http://arxiv.org/pdf/1708.03203
http://arxiv.org/abs/1708.03203
https://zbmath.org/7163562
https://doi.org/10.1002/mma.5777
https://onlinelibrary.wiley.com/doi/abs/10.1002/mma.5777
https://ui.adsabs.harvard.edu/abs/2019MMAS...42.6741H/abstract

A Carleman Function and the Cauchy Problem for the Laplace Equation: A Carleman function and the Cauchy problem for the Laplace equation

Authors: Sharof Yarmukhamedov

Source: Siberian Mathematical Journal. 45:580-595

Subject Terms: Boundary value and inverse problems for harmonic functions in two dimensions, regularization, fundamental solution, Green's formula, Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation, harmonic function, Carleman formula, 0101 mathematics, Boundary value and inverse problems for harmonic functions in higher dimensions, Mittag-Leffler entire function, 01 natural sciences

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Access URL: https://zbmath.org/2112609
https://eudml.org/doc/51055
https://link.springer.com/article/10.1023/B%3ASIMJ.0000028622.69605.c0