SIGMA-MODERATE SOLUTIONS OF LU=U(ALPHA) AND FINE TRACE ON THE BOUNDARY

Authors
KUZNETSOV SE
Citation
Se. Kuznetsov, SIGMA-MODERATE SOLUTIONS OF LU=U(ALPHA) AND FINE TRACE ON THE BOUNDARY, Comptes rendus de l'Academie des sciences. Serie 1, Mathematique, 326(10), 1998, pp. 1189-1194
Citations number
14
Categorie Soggetti
Mathematics,Mathematics
Journal title
Comptes rendus de l'Academie des sciences. Serie 1, Mathematique → ACNP
ISSN journal
07644442
Volume
326
Issue
10
Year of publication
1998
Pages
1189 - 1194
Database
ISI
SICI code
0764-4442(1998)326:10<1189:SSOLAF>2.0.ZU;2-Q
Abstract
We investigate the class of all positive solutions of the equation Lu = u(alpha), 1 < alpha less than or equal to 2 in a smooth domain E sub set of R-d. We define the fine trace tr(u) of a solution u as a pair ( Gamma, nu), where Gamma is a set of singular boundary points of u, and nu is a certain sigma-finite measure on the complement of Gamma. We d escribe all possible traces and we construct the minimal solution with the given trace. (C) Academie des Sciences/Elsevier, Paris.