A Radó Theorem for the Porous Medium Equation

  • We prove that each locally Lipschitz continuous function satisfying the porous medium equation away from the set of its zeroes is actually a weak solution of this equation in the whole domain.

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Author details:Dmitry Fedchenko, Nikolai Nikolaevich TarkhanovORCiDGND
Title of parent work (German):Preprints des Instituts für Mathematik der Universität Potsdam
Publication series (Volume number):Preprints des Instituts für Mathematik der Universität Potsdam (6 (2017) 1)
Publisher:Universitätsverlag Potsdam
Place of publishing:Potsdam
Publication type:Preprint
Year of first publication:2017
Completion year:2017
Publishing institution:Universität Potsdam
Publishing institution:Universitätsverlag Potsdam
Release date:2017/02/08
Tag:porous medium equation; quasilinear equation; removable set
Number of pages:12
Organizational units:Mathematisch-Naturwissenschaftliche Fakultät / Institut für Mathematik
DDC classification:5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik
MSC classification:30-XX FUNCTIONS OF A COMPLEX VARIABLE (For analysis on manifolds, see 58-XX) / 30Cxx Geometric function theory / 30C62 Quasiconformal mappings in the plane
31-XX POTENTIAL THEORY (For probabilistic potential theory, see 60J45) / 31Cxx Other generalizations / 31C45 Other generalizations (nonlinear potential theory, etc.)
35-XX PARTIAL DIFFERENTIAL EQUATIONS / 35Bxx Qualitative properties of solutions / 35B60 Continuation and prolongation of solutions [See also 58A15, 58A17, 58Hxx]
35-XX PARTIAL DIFFERENTIAL EQUATIONS / 35Jxx Elliptic equations and systems [See also 58J10, 58J20] / 35J60 Nonlinear elliptic equations
Collection(s):Universität Potsdam / Schriftenreihen / Preprints des Instituts für Mathematik der Universität Potsdam, ISSN 2193-6943 / 2017
License (German):License LogoUrheberrechtsschutz