Some Non-standard Sobolev Spaces, Interpolation and Its Application to PDE

We consider some nonstandard Sobolev spaces in one dimension, in which functions have different regularity in different subsets. These spaces are useful in the study of some nonlinear parabolic equations where the nonlinearity is highly degenerate and depends on the smoothness of the solution at a c...

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Bibliographic Details
Published in:Acta applicandae mathematicae Vol. 121; no. 1; pp. 57 - 67
Main Authors: González, María del Mar, Gualdani, Maria Pia
Format: Journal Article Publication
Language:English
Published: Dordrecht Springer Netherlands 01.10.2012
Springer Nature B.V
Subjects:
26 Real functions
26A Functions of one variable
35 Partial differential equations
35K Parabolic equations and systems
35S Pseudodifferential operators and other generalizations of partial differential operators
46 Associative rings and algebras
46B Normed linear spaces and Banach spaces; Banach lattices
Applications of Mathematics
Calculus of Variations and Optimal Control; Optimization
Classificació AMS
Computational Mathematics and Numerical Analysis
Data smoothing
Diffusion
Equilibrium
Free boundaries
Functional spaces
Hypotheses
Interpolation
Matemàtiques i estadística
Mathematical analysis
Mathematics
Mathematics and Statistics
Nonlinear equations
Nonlinear parabolic equation
Nonlinearity
Partial Differential Equations
Probability Theory and Stochastic Processes
Regularity
Singularities
Sobolev space
Studies
Àrees temàtiques de la UPC
Interpolation
26A33
35K05
Functional spaces
Nonlinear parabolic equation
35S05
46B70
ISSN:0167-8019, 1572-9036
Online Access:Get full text
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Description
Summary:We consider some nonstandard Sobolev spaces in one dimension, in which functions have different regularity in different subsets. These spaces are useful in the study of some nonlinear parabolic equations where the nonlinearity is highly degenerate and depends on the smoothness of the solution at a certain subset (that may vary with time). An example of application is a diffusion equation with a smooth free boundary, and a moving source/sink where the solution has singularity. The main new idea here is to characterize the functional space setting that is needed for semigroup theory to apply.
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ISSN:0167-8019
1572-9036
DOI:10.1007/s10440-012-9674-6