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The Harnack inequality for second-order elliptic equations with divergence-free drifts
Harnack inequality second-order elliptic equations divergence-free drifts
2015/7/14
We consider an elliptic equation with a divergence-free drift b. We prove that an inequality of Harnack type holds under the assumption b ∈ Ln/2+δ ∩ L2 where δ > 0. As an application we provide a one ...
PRINCIPAL CURVATURE ESTIMATES FOR THE CONVEX LEVEL SETS OF SEMILINEAR ELLIPTIC EQUATIONS
PRINCIPAL CURVATURE ESTIMATES THE CONVEX LEVEL SETS SEMILINEAR ELLIPTIC EQUATIONS
2014/4/3
We give a positive lower bound for the principal curvature of the strict convex level sets of harmonic functions in terms of the principal curvature of the domain boundary and the norm of the boundary...
Cesari-type Conditions for Semilinear Elliptic Equations with Leading Term Containing Controls
optimal control existence conditions elliptic equations homogenization
2011/1/18
An optimal control problem governed by semilinear elliptic partial differential equations is con-sidered. The equation is in divergence form with the leading term containing controls. By studying the ...
On local analytic expansions of densities in the context of (micro-)hypoelliptic and classes of semi-elliptic equations
On local analytic expansions of densities context of (micro-)hypoelliptic classes of semi-elliptic equations
2011/1/17
Explicit representations of densities for linear parabolic partial differential equations are useful in order to design computation schemes of high accuracy for a considerable class of diffusion model...
On non-local reflection for elliptic equations of the second order in R^2 (the Dirichlet condition)
elliptic equations the second order in R^2 (the Dirichlet condition)
2010/12/1
Point-to-point re
ection holding for harmonic functions subject to the Dirichlet or Neumann conditions on an analytic curve in the plane almost always fails for solutions to more general elliptic equ...
Local Estimates for Some Elliptic Equations Arising from Conformal Geometry
Local Estimates Elliptic Equations Arising Conformal Geometry
2018/4/19
We present some local gradient and Hessian estimates from C0 estimates for some elliptic equations arising from conformal deformations on the manifolds with totally geodesic boundary, which generalize...
EXISTENCE AND MULTIPLICITY RESULTS FOR A DEGENERATE ELLIPTIC EQUATIONS
degenerate elliptic equation mountain pass theorem maximal positive solution
2007/12/12
The goal of this paper is to study the multiplicity result of positive solutions of a class of degenerate elliptic equations. On the basis of the mountain pass theorems and the sub- and supersolutions...