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Russian Mathematical Surveys, 2004, Volume 59, Issue 1, Pages 147–157
DOI: https://doi.org/10.1070/RM2004v059n01ABEH000705 (Mi rm705) 		 
This article is cited in 2 scientific papers (total in 2 papers)

Superdiffusions and positive solutions of non-linear partial differential equations

E. B. Dynkin

Cornell University
English version PDF (210 kB) Citations (2) Russian version article
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DOI: https://doi.org/10.1070/RM2004v059n01ABEH000705
Abstract: By using super-Brownian motion, all positive solutions of the non-linear differential equation $\Delta u=u^\alpha$ with $1<\alpha\leqslant 2$ in a bounded smooth domain $E$ are characterized by their (fine) traces on the boundary. This solves a problem posed by the author a few years ago. The special case $\alpha=2$ was treated by B. Mselati in 2002.
Received: 09.09.2003
Bibliographic databases:
Document Type: Article
UDC: 519.218.1
MSC: Primary 35J60, 35B99, 60J60; Secondary 60J65, 35J67, 31C15, 60G57
Language: English
Original paper language: Russian
Citation: E. B. Dynkin, “Superdiffusions and positive solutions of non-linear partial differential equations”, Russian Math. Surveys, 59:1 (2004), 147–157
Citation in format AMSBIB
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\by E.~B.~Dynkin
\paper Superdiffusions and positive solutions of non-linear partial differential equations
\jour Russian Math. Surveys
\yr 2004
\vol 59
\issue 1
\pages 147--157
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  • https://www.mathnet.ru/eng/rm/v59/i1/p145
    • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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