ﻻ يوجد ملخص باللغة العربية
We study the behaviour of Hardy-weights for a class of variational quasi-linear elliptic operators of $p$-Laplacian type. In particular, we obtain necessary sharp decay conditions at infinity on the Hardy-weights in terms of their integrability with respect to certain integral weights. Some of the results are extended also to nonsymmetric linear elliptic operators. Applications to various examples are discussed as well.
We investigate the large-distance asymptotics of optimal Hardy weights on $mathbb Z^d$, $dgeq 3$, via the super solution construction. For the free discrete Laplacian, the Hardy weight asymptotic is the familiar $frac{(d-2)^2}{4}|x|^{-2}$ as $|x|toin
We consider the equation $Delta u=Vu$ in exterior domains in $mathbb{R}^2$ and $mathbb{R}^3$, where $V$ has certain periodicity properties. In particular we show that such equations cannot have non-trivial superexponentially decaying solutions. As an
We prove an existence result for the Poisson equation on non-compact Riemannian manifolds satisfying weighted Poincare inequalities outside compact sets. Our result applies to a large class of manifolds including, for instance, all non-parabolic mani
We investigate existence and uniqueness of bounded solutions of parabolic equations with unbounded coefficients in $Mtimes mathbb R_+$, where $M$ is a complete noncompact Riemannian manifold. Under specific assumptions, we establish existence of solu
We obtain a quantitative high order expansion at infinity of solutions for a family of fully nonlinear elliptic equations on exterior domain, refine the study of the asymptotic behavior of the Monge-Amp`ere equation, the special Lagrangian equation a