Perron's method for the porous medium equation

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 21 Nov 2016Embargo end date: 01 Jan 2014Publisher:European Mathematical Society - EMS - Publishing House GmbHJournal:Journal of the European Mathematical Society, volume 18, pages 2,953-2,969 (issn: 1435-9855, eissn: 1435-9863,

Copyright policy )

Authors: Lukkari, Teemu; Lindqvist; Peter; Kinnunen, Juha;

doi: 10.4171/jems/658 , 10.48550/arxiv.1401.4277

arXiv: 1401.4277

Perron's method for the porous medium equation

- Summary
- Subjects
- Metrics

Abstract

This work extends Perron’s method for the porous medium equation in the slow diffusion case. The main result shows that nonnegative continuous boundary functions are resolutive in a general cylindrical domain.

Related Organizations

University of Jyväskylä
Finland
Aalto University
Finland
Norwegian University of Science and Technology
Norway

Keywords

ta111, comparison principle, Perron method, Primary 35K55, Secondary 35K65, 35K20, 31C45, Degenerate parabolic equations, obstacles, Porous medium equation, Mathematics - Analysis of PDEs, porous medium equation, Initial-boundary value problems for second-order parabolic equations, FOS: Mathematics, Nonlinear parabolic equations, Other generalizations (nonlinear potential theory, etc.), Analysis of PDEs (math.AP)

Impact byBIP!

	selected citations These citations are derived from selected sources. This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).	10
	popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.	Top 10%
	influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).	Average
	impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.	Top 10%