Results 21 to 25 of about 479 (25)

The fundamental solution of nonlinear equations with natural growth terms [PDF]

arXiv, 2010
We find bilateral global bounds for the fundamental solutions associated with some quasilinear and fully nonlinear operators perturbed by a nonnegative zero order term with natural growth. In addition, we consider the Sobolev regularity of the fundamental solution away from its pole.
arxiv  

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  

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