Parabolic Capacity and Soft Measures for Nonlinear Equations

Jérôme Droniou; Alessio Porretta; Alain Prignet

doi:10.1023/A:1023248531928

Parabolic Capacity and Soft Measures for Nonlinear Equations

Jérôme Droniou, Alessio Porretta, Alain Prignet

Research output: Contribution to journal › Article › Research › peer-review

105 Citations (Scopus)

Abstract

We first introduce, using a functional approach, the notion of capacity related to the parabolic p-Laplace operator. Then we prove a decomposition theorem for measures (in space and time) that do not charge the sets of null capacity. We apply this result to prove existence and uniqueness of renormalized solutions for nonlinear parabolic initial boundary-value problems with such measures as right-hand side.

Original language	English
Pages (from-to)	99-161
Number of pages	63
Journal	Potential Analysis
Volume	19
Issue number	2
DOIs	https://doi.org/10.1023/A:1023248531928
Publication status	Published - 1 Sept 2003
Externally published	Yes

Keywords

Capacity
Measure
Parabolic equations

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10.1023/A:1023248531928

Cite this

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AB - We first introduce, using a functional approach, the notion of capacity related to the parabolic p-Laplace operator. Then we prove a decomposition theorem for measures (in space and time) that do not charge the sets of null capacity. We apply this result to prove existence and uniqueness of renormalized solutions for nonlinear parabolic initial boundary-value problems with such measures as right-hand side.

KW - Capacity

KW - Measure

KW - Parabolic equations

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DO - 10.1023/A:1023248531928

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JO - Potential Analysis

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Parabolic Capacity and Soft Measures for Nonlinear Equations

Abstract

Keywords

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