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Dirichlet Boundary Conditions for Degenerate and Singular Nonlinear Parabolic Equations

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Abstract

We study existence and uniqueness of solutions to a class of quasilinear degenerate parabolic equations, in bounded domains. We show that there exists a unique solution which satisfies possibly inhomogeneous Dirichlet boundary conditions. To this purpose some barrier functions are properly introduced and used.

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Authors and Affiliations

  1. Dipartimento di Matematica e Informatica, Università della Calabria, via P. Bucci 31B, 87036, Rende, CS, Italy

    Fabio Punzo

  2. Université Paris-Diderot Institut de Mathématiques de Jussieu-Paris Rive Gauche, batiment Sophie Germain, 5 rue Thomas Mann., 75205, Paris Cedex 13, France

    Marta Strani

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  1. Fabio Punzo
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  2. Marta Strani
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Correspondence to Marta Strani.

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Punzo, F., Strani, M. Dirichlet Boundary Conditions for Degenerate and Singular Nonlinear Parabolic Equations. Potential Anal 47, 151–168 (2017). https://doi.org/10.1007/s11118-016-9611-9

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  • DOI: https://doi.org/10.1007/s11118-016-9611-9

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