Results 21 to 25 of about 646 (25)

Topics in the theory of positive solutions of second-order elliptic and parabolic partial differential equations [PDF]

arXiv, 2005
The purpose of the paper is to review a variety of recent developments in the theory of positive solutions of general linear elliptic and parabolic equations of second-order on noncompact Riemannian manifolds, and to point out a number of their consequences.
arxiv  

Elliptic differential equations with measurable coefficients [PDF]

arXiv, 2005
We prove the unique solvability of second order elliptic equations in non-divergence form in Sobolev spaces. The coefficients of the second order terms are measurable in one variable and VMO in other variables. From this result, we obtain the weak uniqueness of the martingale problem associated with the elliptic equations.
arxiv  

Nonremovable sets for Hölder continuous quasiregular mappings in the plane [PDF]

arXiv, 2006
We show that for any dimension t>2(1+alpha K)/(1+K) there exists a compact set E of dimension t and a function alpha-Holder continuous on the plane, which is K-quasiregular only outside of E. To do this, we construct an explicit K-quasiconformal mapping that gives, by one side, extremal dimension distortion on a Cantor-type set, and by the other, more ...
arxiv  

A Visual Approach to the Regularity Theory for Fully Nonlinear Elliptic Equations [PDF]

arXiv
We revisit the regularity theory for uniformly elliptic equations.
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