BOUNDARY TRACE OF POSITIVE SOLUTIONS OF N ONLINEAR ELLIPTIC-EQUATIONS

Authors
MARCUS M VERON L
Citation
M. Marcus et L. Veron, BOUNDARY TRACE OF POSITIVE SOLUTIONS OF N ONLINEAR ELLIPTIC-EQUATIONS, Comptes rendus de l'Academie des sciences. Serie 1, Mathematique, 321(2), 1995, pp. 179-184
Citations number
7
Categorie Soggetti
Mathematics, General",Mathematics
Journal title
Comptes rendus de l'Academie des sciences. Serie 1, Mathematique → ACNP
ISSN journal
07644442
Volume
321
Issue
2
Year of publication
1995
Pages
179 - 184
Database
ISI
SICI code
0764-4442(1995)321:2<179:BTOPSO>2.0.ZU;2-Z
Abstract
Let B be the unit open ball in R(N) and u a positive solution of (E) : -Delta u + u(q) = 0, q > 1, in B. We prove that it is possible to def ine the trace of u on partial derivative B by a unique couple (S, mu) where S is a closed subset of partial derivative B and mu is a Radon m easure on R = partial derivative B\S. The set S is the singular set of the trace of a and the set R is the regular set where the trace of u is mu.