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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 ...
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...
We introduce a class of weak solutions to the quasilinear equation $-\Delta_p u = \sigma |u|^{p-2}u$ in an open set $\Omega\subset\mathbf{R}^n$. Here $p>1$, and $\Delta_p u$ is the $p$-Laplacian opera...
This monograph concerns linear and nonlinear Dirichlet problems involving L^1 data and more generally measure data, based on Stampacchia's definition of weak solution. We explain some of the main tool...
Abstract: In this paper we study some weighted isoperimetric inequalities relative to cones of $\mathbb{R}^{N}$. We give some information on the structure of those measures admitting as isoperimetric ...
Abstract: A monotonicity approach to the study of the asymptotic behavior near corners of solutions to semilinear elliptic equations in domains with a conical boundary point is discussed. The presence...
Abstract: We establish existence and qualitative properties of saddle-shaped solutions of the elliptic fractional equation $(-\Delta)^{1/2}u=f(u)$ in all the space $\re^{2m}$, where $f$ is of bistable...
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 ...
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...
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...
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...
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...
In this paper, we consider the principal eigenvalue problem for Hormander's Laplacian on $R^n$, and we find a comparison principle for such principal eigenvalues. We also study a related semi-linear s...

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