Results 91 to 100 of about 1,349 (111)

On subsolutions and concavity for fully nonlinear elliptic equations

Advanced Nonlinear Studies
Subsolutions and concavity play critical roles in classical solvability, especially a priori estimates, of fully nonlinear elliptic equations. Our first primary goal in this paper is to explore the possibility to weaken the concavity condition.
Guan Bo
doaj   +1 more source

Liouville Type Theorems for Minimal Surface Equations in Half Space [PDF]

arXiv, 2019
For $n\geq2,$ we obtain Liouville type theorems for minimal surface equations in half space $\mathbf R^n_+$ with affine Dirichlet boundary value or constant Neumann boundary value.
arxiv  

Non linear elliptic theory and the Monge-Ampere equation [PDF]

Proceedings of the ICM, Beijing 2002, vol. 1, 179--187, 2002
The Monge-Ampere equation, plays a central role in the theory of fully non linear equations. In fact we will like to show how the Monge-Ampere equation, links in some way the ideas comming from the calculus of variations and those of the theory of fully non linear equations.
arxiv  

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  

A New H ² Regularity Condition of the Solution to Dirichlet Problem of the Poisson Equation and Its Applications. [PDF]

Acta Math Sin Engl Ser, 2020
Gao FC, Lai MJ.
europepmc   +1 more source

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  

Spectral shift functions and Dirichlet-to-Neumann maps. [PDF]

Math Ann, 2018
Behrndt J, Gesztesy F, Nakamura S.
europepmc   +1 more source

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