4,241 research outputs found
Existence and Spectral Theory for Weak Solutions of Neumann and Dirichlet Problems for Linear Degenerate Elliptic Operators with Rough Coefficients
In this paper we study existence and spectral properties for weak solutions
of Neumann and Dirichlet problems associated to second order linear degenerate
elliptic partial differential operators , with rough coefficients of the
form in a geometric
homogeneous space setting where the matrix function is
allowed to degenerate. We give a maximum principle for weak solutions of
and follow this with a result describing a relationship between
compact projection of the degenerate Sobolev space into and a
Poincar\'e inequality with gain adapted to
Nonexistence of stable solutions to quasilinear elliptic equations on Riemannian manifolds
We prove nonexistence of nontrivial, possibly sign changing, stable solutions
to a class of quasilinear elliptic equations with a potential on Riemannian
manifolds, under suitable weighted volume growth conditions on geodesic balls
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