Hardy–Sobolev critical elliptic equations with boundary singularities
Harmonic averages, exact difference schemes and local Green’s functions in variable coefficient PDE problems
A brief survey is given to show that harmonic averages enter in a natural way in the numerical solution of various variable coefficient problems, such as in elliptic and transport equations, also of singular perturbation types. Local Green’s functions used as test functions in the Petrov-Galerkin finite element method combined with harmonic averages can be very efficient and are related to exact difference schemes.
Harmonic Mappings and Minimal Submanifolds.
Harmonic measures of perforated domains
Harmonic synthesis of solutions of elliptic equation with periodic coefficients
An elliptic system in , which is invariant under the action of the group is considered. We construct a holomorphic family of finite-dimensional subrepresentations of the group in the space of solutions (Floquet solutions), such that any solution of the growth at infinity can be rewritten in the form of an integral over the family.
Harmonické funkce a věty o průměru
Harnachk Inequalities for Solutions of General Second Order Parabolic Equations and Estimates of Their Hölder Constants.
Harnack estimates for weak supersolutions to nonlinear degenerate parabolic equations
In this work we prove both local and global Harnack estimates for weak supersolutions to second order nonlinear degenerate parabolic partial differential equations in divergence form. We reduce the proof to an analysis of so-called hot and cold alternatives, and use the expansion of positivity together with a parabolic type of covering argument. Our proof uses only the properties of weak supersolutions. In particular, no comparison to weak solutions is needed.
Harnack inequalities and ABP estimates for nonlinear second-order elliptic equations in unbounded domains.
Harnack inequalities, exponential separation, and perturbations of principal Floquet bundles for linear parabolic equations
Harnack Inequalities for Nonuniformly Elliptic Divergence Structure Equations.
Harnack inequalities for quasi-minima of variational integrals
Harnack inequalities for Schrödinger operators
Harnack inequalities on graphs
Harnack inequality and Green function for a certain class of degenerate elliptic differential operators.
The main purpose of this work is to obtain a Harnack inequality and estimates for the Green function for the general class of degenerate elliptic operators described below.
Harnack inequality for hypoelliptic ultraparabolic equations with a singular lower order term.
Harnack inequality for the Schrödinger problem relative to strongly local Riemannian -homogeneous forms with a potential in the Kato class.
Harnack type estimates for nonlinear elliptic systems and applications
Harnack's estimates: positivity and local behavior of degenerate and singular parabolic equations.
Harnack’s inequalities for solutions to the mean curvature equation and to the capillarity problem