Premium
An elliptic boundary problem in a half–space
Author(s) -
Faierman Melvin,
Möller Manfred
Publication year - 2003
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.200310075
Subject(s) - mathematics , sobolev space , weight function , boundary value problem , mathematical analysis , boundary (topology) , a priori and a posteriori , function (biology) , space (punctuation) , function space , pure mathematics , philosophy , linguistics , epistemology , evolutionary biology , biology
The spectral theory for general non–selfadjoint elliptic boundary problems involving a discontinuous weight function has been well developed under certain restrictions concerning the weight function. In the course of extending the results so far established to a more general weight function, there arises the problem of establishing, in an L p Sobolev space setting, the existence of and a priori estimates for solutions for a boundary problem for the half–space ℝ n + involving a weight function which vanishes at the boundary x n = 0. In this paper we resolve this problem.