Results 81 to 85 of about 1,014 (85)

Best constants in Poincaré inequalities for convex domains [PDF]

arXiv, 2011
We prove a Payne-Weinberger type inequality for the $p$-Laplacian Neumann eigenvalues ($p\ge 2$). The inequality provides the sharp upper bound on convex domains, in terms of the diameter alone, of the best constants in Poincar\'e inequality. The key point is the implementation of a refinement of the classical P\'olya-Szeg\"o inequality for the ...
arxiv  

Existence of nontrivial weak solutions for a quasilinear Choquard equation. [PDF]

J Inequal Appl, 2018
Lee J, Kim JM, Bae JH, Park K.
europepmc   +1 more source

A Symmetry problem for some quasi-linear equations in Euclidean space [PDF]

arXiv
We prove sharp asymptotic estimates for the gradient of positive solutions to certain nonlinear $p$-Laplace equations in Euclidean space by showing symmetry and uniqueness of positive solutions to associated limiting problems.
arxiv  

An inhomogeneous p-laplacian equation with a Hardy potential [PDF]

arXiv
In this work we study the existence and regularity of solutions to the following equation: $$-\Delta_p u + g(x) u = \frac{\lambda}{|x|^{p}} |u|^{p-2}u + f,$$ where $1< p < N$ and $f\in L^m$, where $m\ge 1$.
arxiv