A Radó Theorem for the Porous Medium Equation

Fedchenko, Dmitry; Tarkhanov, Nikolai Nikolaevich

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A Radó Theorem for the Porous Medium Equation

Dmitry Fedchenko, Nikolai Nikolaevich Tarkhanov

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.

Metadaten
Author details:	Dmitry Fedchenko, Nikolai Nikolaevich Tarkhanov ORCiD GND
URN:	urn:nbn:de:kobv:517-opus4-102735
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
Language:	English
Year of first publication:	2017
Publication year:	2017
Publishing institution:	Universität Potsdam
Publishing institution:	Universitätsverlag Potsdam
Release date:	2017/02/08
Tag:	porous medium equation; quasilinear equation; removable set
Volume:	6
Issue:	1
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):	Keine öffentliche Lizenz: Unter Urheberrechtsschutz

A Radó Theorem for the Porous Medium Equation

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