473 research outputs found
Isolated Singularities of Polyharmonic Inequalities
We study nonnegative classical solutions of the polyharmonic inequality
in a punctured neighborhood of the origin in . We give
necessary and sufficient conditions on integers and such that
these solutions satisfy a pointwise a priori bound as .Comment: 18 page
Pointwise Bounds and Blow-up for Systems of Semilinear Elliptic Inequalities at an Isolated Singularity via Nonlinear Potential Estimates
We study the behavior near the origin of positive solutions and
of the system
in where
are continuous functions. We provide optimal
conditions on and at such that solutions of this system
satisfy pointwise bounds near the origin. In dimension we show that this
property holds if or grow at most linearly at infinity. In
dimension and under the assumption ,
as , (), we obtain a new
critical curve that optimally describes the existence of such pointwise bounds.
Our approach relies in part on sharp estimates of nonlinear potentials which
appear naturally in this context.Comment: 41 pages, 1 figur
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