This article is cited in 4 papers

Superdiffusions and positive solutions of non-linear partial differential equations

E. B. Dynkin

Cornell University

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.

UDC: 519.218.1

MSC: Primary 35J60, 35B99, 60J60; Secondary 60J65, 35J67, 31C15, 60G57

Received: 09.09.2003

DOI: 10.4213/rm705

 English version: Russian Mathematical Surveys, 2004, 59:1, 147–157

Bibliographic databases:

• 
• 
• 
• 
•