, Volume 132, Issue 1, pp 125168
First online:
On positivity of solutions of degenerate boundary value problems for secondorder elliptic equations
 Yehuda PinchoverAffiliated withDepartment of Mathematics, TechnionIsrael Institute of Technology Email author
 , Tiferet Saadon (Suez)Affiliated withDepartment of Mathematics, TechnionIsrael Institute of Technology
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In this paper we study thedegenerate mixed boundary value problem:Pu=f in Ω,B _{ u }=gon Ω∂Г where ω is a domain in ℝ^{ n },P is a second order linear elliptic operator with real coefficients, Γ⊆∂Ω is a relatively closed set, andB is an oblique boundary operator defined only on ∂Ω/Γ which is assumed to be a smooth part of the boundary.
The aim of this research is to establish some basic results concerning positive solutions. In particular, we study the solvability of the above boundary value problem in the class of nonnegative functions, and properties of the generalized principal eigenvalue, the ground state, and the Green function associated with this problem. The notion of criticality and subcriticality for this problem is introduced, and a criticality theory for this problem is established. The analogs for the generalized Dirichlet boundary value problem, where Γ=∂Ω, were examined intensively by many authors.
 Title
 On positivity of solutions of degenerate boundary value problems for secondorder elliptic equations
 Journal

Israel Journal of Mathematics
Volume 132, Issue 1 , pp 125168
 Cover Date
 200212
 DOI
 10.1007/BF02784508
 Print ISSN
 00212172
 Online ISSN
 15658511
 Publisher
 SpringerVerlag
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 Authors

 Yehuda Pinchover ^{(1)}
 Tiferet Saadon (Suez) ^{(1)}
 Author Affiliations

 1. Department of Mathematics, TechnionIsrael Institute of Technology, 32000, Haifa, Israel