Citation: Boundary Value Problems 2007 2007:042548
Harnack's Estimates, Positivity and Local Behavior of Degenerate and Singular Parabolic Equations
Liouville Theorems for a Class of Linear Second-Order Operators with Nonnegative Characteristic Form
We report on some Liouville-type theorems for a class of linear second-order partial differential equation with nonnegative characteristic form. The theorems we show improve our previous results.
Citation: Boundary Value Problems 2007 2007:048232
Harnack Inequality for the Schrödinger Problem Relative to Strongly Local Riemannian -Homogeneous Forms with a Potential in the Kato Class
We define a notion of Kato class of measures relative to a Riemannian strongly local -homogeneous Dirichlet form and we prove a Harnack i...
Citation: Boundary Value Problems 2007 2007:024806
The aim of this article is to give an introduction to certain inequalities named after Carl Gustav Axel von Harnack. These inequalities were originally defined for harmonic functions in the plane and much late...
Citation: Boundary Value Problems 2007 2007:081415
We prove a boundary comparison principle for positive infinity-harmonic functions for smooth boundaries. As consequences, we obtain (a) a doubling property for certain positive infinity-harmonic functions in s...
Citation: Boundary Value Problems 2007 2007:078029
We prove interior gradient estimates for a large class of parabolic equations in divergence form. Using some simple ideas, we prove these estimates for several types of equations that are not amenable to previ...
Citation: Boundary Value Problems 2007 2007:035825
Subsolutions of Elliptic Operators in Divergence Form and Application to Two-Phase Free Boundary Problems
Let be a divergence form operator with Lipschitz continuous coefficients in a domain ...
Citation: Boundary Value Problems 2006 2007:057049
A theorem on removable singularities of -differential forms is proved and applied to quasiregular mappings.
Citation: Boundary Value Problems 2006 2007:061602
We establish the global Hölder estimates for solutions to second-order elliptic equations, which vanish on the boundary, while the right-hand side is allowed to be unbounded. For nondivergence elliptic equatio...
Citation: Boundary Value Problems 2006 2007:057928
We investigate the Dirichlet problem for the parabolic equation in a nonsmooth and closed domain
Citation: Boundary Value Problems 2006 2007:031261
We study overdetermined boundary conditions for positive solutions to some elliptic partial differential equations of -Laplacian type in ...
Citation: Boundary Value Problems 2006 2007:030190
We investigate local and global properties of positive solutions to the fast diffusion equation in the good exponent range
Citation: Boundary Value Problems 2006 2007:021425
We show that every weak supersolution of a variable exponent -Laplace equation is lower semicontinuous and that the singular set of such ...
Citation: Boundary Value Problems 2006 2007:048348