Search Results - "Boundary value problems for second-order elliptic equations"

Multiplicities of eigenvalues for the Laplace operator on a square

Authors: Fu, Siqi Heimrath, Jack Hsiao, Samuel

Source: Involve, a Journal of Mathematics. 18:487-494

Subject Terms: Boundary value problems for second-order elliptic equations, Laplace operator, eigenvalue, multiplicity, Estimates of eigenvalues in context of PDEs, Legendre's formula

File Description: application/xml

Access URL: https://zbmath.org/8035722
https://doi.org/10.2140/involve.2025.18.487

Modeling Floral and Arthropod Electrostatics Using a Two-Domain AAA-Least Squares Algorithm: Modeling floral and arthropod electrostatics using a two-domain AAA-least squares algorithm

Authors: Samuel J. Harris Ryan A. Palmer N. R. McDonald

Source: Harris, S, Palmer, R A & McDonald, R 2025, 'Modeling Floral and Arthropod Electrostatics Using a Two-Domain AAA-Least Squares Algorithm', SIAM Journal on Applied Mathematics, vol. 85, no. 2, pp. 916-944. https://doi.org/10.48550/arXiv.2411.02195, https://doi.org/10.1137/24M1638021

Subject Terms: Boundary value problems for second-order elliptic equations, Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation, mixed boundary value problem, Biological Physics (physics.bio-ph), Soft Condensed Matter (cond-mat.soft), FOS: Physical sciences, plant-pollinator ecology, Physics - Biological Physics, Applications of PDE in areas other than physics, Condensed Matter - Soft Condensed Matter, electroreception, electrostatics, AAA-least squares

File Description: application/xml; application/pdf

Access URL: http://arxiv.org/abs/2411.02195
https://zbmath.org/8035700
https://doi.org/10.1137/24m1638021
https://research-information.bris.ac.uk/en/publications/96487b29-216b-4d27-97a3-1453e0e6e480
https://hdl.handle.net/1983/96487b29-216b-4d27-97a3-1453e0e6e480

Frequency Range of a Non-Lipschitz Parametric Optimization of a Noise Absorption: Frequency range of a non-Lipschitz parametric optimization of a noise absorption

Authors: Frédéric Magoulès Mathieu Menoux Anna Rozanova-Pierrat

Source: SIAM Journal on Control and Optimization. 63:1267-1285

Subject Terms: Linear equations (linear algebraic aspects), Iterative numerical methods for linear systems, Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation, Boundary value problems for second-order elliptic equations, sound absorption, wave propagation, \(d\)-upper regular measure, parametric shape optimization, Helmholtz equation, Numerical solution of discretized equations for boundary value problems involving PDEs, Robin boundary condition, First-order hyperbolic systems

File Description: application/xml

Concentrating Bound States for Singularly Perturbed Nonlinear Dirichlet Problems Involving Critical Growth: Concentrating bound states for singularly perturbed nonlinear Dirichlet problems involving critical growth

Authors: Yi He Jianjun Zhang

Source: SIAM Journal on Mathematical Analysis. 57:1832-1865

Subject Terms: Variational methods for second-order elliptic equations, concentration, Variational methods applied to PDEs, single-peak solutions, Boundary value problems for second-order elliptic equations, Semilinear elliptic equations, Abstract critical point theory (Morse theory, Lyusternik-Shnirel'man theory, etc.) in infinite-dimensional spaces, distance function, singularly perturbed, Singular perturbations in context of PDEs, Dirichlet problem

File Description: application/xml

Access URL: https://zbmath.org/8035707
https://doi.org/10.1137/24m1675898

A High-Order Perturbation of Envelopes (HOPE) Method for Vector Electromagnetic Scattering by Periodic Inhomogeneous Media: Joint Analyticity: A high-order perturbation of envelopes (HOPE) method for vector electromagnetic scattering by periodic inhomogeneous media: joint analyticity

Authors: David P. Nicholls Liet Vo

Source: SIAM Journal on Applied Mathematics. 85:755-778

Subject Terms: Spectral, collocation and related methods applied to problems in optics and electromagnetic theory, high-order spectral methods, Boundary value problems for second-order elliptic equations, Maxwell equations, inhomogeneous media, high-order perturbation of envelopes methods, linear wave scattering, Spectral, collocation and related methods for boundary value problems involving PDEs, layered media, PDEs in connection with optics and electromagnetic theory, PDEs in connection with geophysics, Diffraction, scattering

File Description: application/xml

Access URL: https://zbmath.org/8035693
https://doi.org/10.1137/24m1643189

L p Carleman estimates for elliptic boundary value problems and applications to the quantification of unique continuation: \(L^p\) Carleman estimates for elliptic boundary value problems and applications to the quantification of unique continuation

Authors: Dehman, Belhassen Ervedoza, Sylvain Thabouti, Lotfi

Source: Annales Henri Lebesgue. 7:1603-1668

Subject Terms: elliptic boundary value problems, Boundary value problems for second-order elliptic equations, Carleman estimates, A priori estimates in context of PDEs

File Description: application/xml

Access URL: https://zbmath.org/8012980
https://doi.org/10.5802/ahl.226

Weak coupling and spectral instability for Neumann Laplacians

Authors: Behrndt, Jussi Gesztesy, Fritz de Snoo, Henk

Source: Proceedings of the American Mathematical Society. 153:1675-1686

Subject Terms: Birman-Schwinger principle, Schrödinger operator, Mathematics - Spectral Theory, Birman–Schwinger principle, Schrödinger operator, Schrödinger equation, Boundary value problems for second-order elliptic equations, Neumann Laplacian, FOS: Mathematics, weakly coupled bound state, Spectrum, resolvent, Spectral Theory (math.SP), spectral instability, Weakly coupled bound state

File Description: application/xml

Access URL: http://arxiv.org/abs/2406.18911
https://research.rug.nl/en/publications/b837cecc-cbb5-4754-bbab-9a7a661967ca
https://doi.org/10.1090/proc/17115
https://hdl.handle.net/11370/b837cecc-cbb5-4754-bbab-9a7a661967ca

The fourth term of the asymptotic behavior near the boundary of a large solution to semilinear Poisson equation with double-power nonlinearity

Authors: Kazuhiro Takimoto Yuxiao Zhang

Source: Analysis. 45:149-160

Subject Terms: Blow-up in context of PDEs, Boundary value problems for second-order elliptic equations, Asymptotic behavior of solutions to PDEs, semilinear Poisson equation, asymptotic behavior, large solution, double-power nonlinearity

File Description: application/xml

Increasing Stability for Recovering Anisotropic Potential in Elastic Scattering from a Linearized Dirichlet to Neumann Map: Increasing stability for recovering anisotropic potential in elastic scattering from a linearized Dirichlet to Neumann map

Authors: Tianjiao Wang Chen Qing Xiang Xu

Source: SIAM Journal on Imaging Sciences. 18:359-387

Subject Terms: Inverse problems for PDEs, increasing stability, Boundary value problems for second-order elliptic equations, inverse elastic scattering, Scattering theory for PDEs, inverse potential, General spectral theory of ordinary differential operators

File Description: application/xml

Spectral ratios and gaps for Steklov eigenvalues of balls with revolution-type metrics

Authors: Jade Brisson Bruno Colbois Katie Gittins

Source: Canadian Mathematical Bulletin. 68:492-511

Subject Terms: Mathematics - Spectral Theory, Boundary value problems for second-order elliptic equations, 35P15, 58C40, Steklov eigenvalues, spectral ratios, spectral gaps, FOS: Mathematics, Estimates of eigenvalues in context of PDEs, Spectral theory, eigenvalue problems on manifolds, Spectral Theory (math.SP)

File Description: application/xml

Access URL: http://arxiv.org/abs/2403.13426
https://zbmath.org/8030874
https://doi.org/10.4153/s0008439524000778

Some remarks on critical sets of Laplace eigenfunctions

Authors: Judge, Chris Mondal, Sugata

Source: Annales mathématiques du Québec. 49:155-163

Subject Terms: Mathematics - Differential Geometry, 0301 basic medicine, critical point, General topics in linear spectral theory for PDEs, 01 natural sciences, 58J05, 03 medical and health sciences, Mathematics - Analysis of PDEs, Boundary value problems for second-order elliptic equations, Differential Geometry (math.DG), FOS: Mathematics, eigenfunction, Laplacian, 0101 mathematics, Analysis of PDEs (math.AP)

File Description: application/xml

Access URL: http://arxiv.org/abs/2204.11968

A Strong Comparison Principle for the Generalized Dirichlet Problem for Monge–Ampère: A strong comparison principle for the generalized Dirichlet problem for Monge-Ampère

Authors: Froese Hamfeldt, Brittany

Source: SIAM Journal on Mathematical Analysis. 57:1-13

Subject Terms: numerical analysis, Comparison principles in context of PDEs, comparison principle, Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness, Degenerate elliptic equations, Monge-Ampère equation, Nonlinear elliptic equations, Monge-Ampère equations, Viscosity solutions to PDEs, Second-order elliptic equations, Mathematics - Analysis of PDEs, Boundary value problems for second-order elliptic equations, FOS: Mathematics, Analysis of PDEs (math.AP)

File Description: application/xml

Access URL: http://arxiv.org/abs/2306.01532
https://zbmath.org/7965641
https://doi.org/10.1137/23m1577006

Three-dimensional nonlinear problems with lack of compactness and mixed boundary conditions

Authors: Alghanemi, Azeb Mahmoud, Randa Ben Chtioui, Hichem

Source: Communications on Pure and Applied Analysis. 24:1566-1589

Subject Terms: Variational methods for second-order elliptic equations, critical variational problems, Boundary value problems for second-order elliptic equations, Laplace operator, blow-up phenomena, mixed boundary conditions, lack of compactness, Nonlinear elliptic equations

File Description: application/xml

Access URL: https://zbmath.org/8035397
https://doi.org/10.3934/cpaa.2025049

Nodal sets of Laplacian eigenfunctions with an eigenvalue of multiplicity 2

Authors: Lyons, Andrew

Source: Annales mathématiques du Québec. 49:105-153

Subject Terms: nodal set, Mathematics - Analysis of PDEs, Boundary value problems for second-order elliptic equations, 35P99, Laplacian eigenfunction, 35P99, 35J25, Hadamard variation, eigenvalue multiplicity, FOS: Mathematics, General topics in linear spectral theory for PDEs, Analysis of PDEs (math.AP)

File Description: application/xml

Access URL: http://arxiv.org/abs/2312.05369

Asymptotic expansions for harmonic functions at conical boundary points

Authors: Dennis Kriventsov Zongyuan Li

Source: Revista Matemática Iberoamericana. 41:837-866

Subject Terms: harmonic, Mathematics - Analysis of PDEs, Boundary value problems for second-order elliptic equations, 35J25, FOS: Mathematics, 0101 mathematics, unique continuation, 01 natural sciences, blow-up, Dirichlet problem, Analysis of PDEs (math.AP)

File Description: application/xml

Access URL: http://arxiv.org/abs/2307.10517
https://zbmath.org/8037296
https://doi.org/10.4171/rmi/1513

Nonexistence of radial positive solutions for a class of nonpositone problems in a ball

Authors: Said Hakimi Hajar Chahi

Source: Monatshefte für Mathematik. 206:885-891

Subject Terms: semilinear equation with Laplacian, Boundary value problems for second-order elliptic equations, Existence problems for PDEs: global existence, local existence, non-existence, Dirichlet problem, non-existence of radial positive solutions

File Description: application/xml

Access URL: https://zbmath.org/8012259
https://doi.org/10.1007/s00605-024-02025-2

Integral formulation of Klein–Gordon singular waveguides: Integral formulation of Klein-Gordon singular waveguides

Authors: Bal, Guillaume Hoskins, Jeremy Quinn, Solomon et al.

Source: Communications on Pure and Applied Mathematics. 78:323-365

Subject Terms: Numerical methods for partial differential equations, boundary value problems, FOS: Physical sciences, Mathematical Physics (math-ph), Numerical Analysis (math.NA), 01 natural sciences, Mathematics - Analysis of PDEs, Boundary value problems for second-order elliptic equations, FOS: Mathematics, Klein-Gordon equation, boundary integral equation, Mathematics - Numerical Analysis, 0101 mathematics, algorithm for solving integral equations, Mathematical Physics, Analysis of PDEs (math.AP)

File Description: application/xml

Access URL: http://arxiv.org/abs/2212.12619

Domain Decomposition Learning Methods for Solving Elliptic Problems: Domain decomposition learning methods for solving elliptic problems

Authors: Sun, Qi Xu, Xuejun Yi, Haotian

Source: SIAM Journal on Scientific Computing. 46:A2445-A2474

Subject Terms: Multigrid methods, domain decomposition for boundary value problems involving PDEs, 02 engineering and technology, Numerical Analysis (math.NA), Neural networks for/in biological studies, artificial life and related topics, neural networks, elliptic PDEs, 01 natural sciences, compensated deep Ritz method, domain decomposition methods, Variational methods applied to PDEs, Boundary value problems for second-order elliptic equations, 0202 electrical engineering, electronic engineering, information engineering, FOS: Mathematics, Mathematics - Numerical Analysis, 0101 mathematics, Artificial neural networks and deep learning

File Description: application/xml

Access URL: http://arxiv.org/abs/2207.10358
https://zbmath.org/7894731
https://doi.org/10.1137/22m1515392

On Ventcel transmission conditions for a Helmholtz problem with a high contrast thin ring

Authors: Khaled El-Ghaouti Boutarene

Source: Rendiconti del Circolo Matematico di Palermo Series 2. 74

Subject Terms: Ventcel transmission conditions, thin layer, asymptotic analysis, Asymptotic approximations, asymptotic expansions (steepest descent, etc.), Boundary value problems for second-order elliptic equations, Asymptotic behavior of solutions to PDEs, Asymptotic analysis in optics and electromagnetic theory, Helmholtz equation, Elliptic equations and elliptic systems, Asymptotic expansions of solutions to PDEs

File Description: application/xml

Access URL: https://zbmath.org/8037011
https://doi.org/10.1007/s12215-025-01230-8

On the Magnetic Dirichlet to Neumann Operator on the Disk: Strong Diamagnetism and Strong Magnetic Field Limit: On the magnetic Dirichlet to Neumann operator on the disk: strong diamagnetism and strong magnetic field limit

Authors: Bernard Helffer François Nicoleau

Source: The Journal of Geometric Analysis. 35

Subject Terms: Dirichlet-to-Neumann operator, FOS: Physical sciences, magnetic field, Mathematical Physics (math-ph), diamagnetism, Mathematics - Spectral Theory, Mathematics - Analysis of PDEs, Schrödinger operator, Schrödinger equation, Boundary value problems for second-order elliptic equations, FOS: Mathematics, 35P20, 35Q40, Spectral Theory (math.SP), Mathematical Physics, Selfadjoint operator theory in quantum theory, including spectral analysis, Analysis of PDEs (math.AP)

File Description: application/xml

Access URL: http://arxiv.org/abs/2411.15522