Estimates for derivatives of the Green functions on homogeneous manifolds of negative curvature.
Estimates for -Hessian operator and some applications
The -convex functions are the viscosity subsolutions to the fully nonlinear elliptic equations , where is the elementary symmetric function of order , , of the eigenvalues of the Hessian matrix . For example, is the Laplacian and is the real Monge-Ampère operator det , while -convex functions and -convex functions are subharmonic and convex in the classical sense, respectively. In this paper, we establish an approximation theorem for negative -convex functions, and give several...
Estimates for the Green function and existence of positive solutions for higher-order elliptic equations.
Estimates for the Poisson kernel on higher rank NA groups
We obtain an estimate for the Poisson kernel for the class of second order left-invariant differential operators on higher rank NA groups.
Estimates for the Poisson kernels and their derivatives on rank one NA groups
For rank one solvable Lie groups of the type NA estimates for the Poisson kernels and their derivatives are obtained. The results give estimates on the Poisson kernel and its derivatives in a natural parametrization of the Poisson boundary (minus one point) of a general homogeneous, simply connected manifold of negative curvature.
Estimates of Green functions and harmonic measures for elliptic operators with singular drift terms.
Estimates of Green functions and their applications for parabolic operators with singular potentials
We prove global pointwise estimates for the Green function of a parabolic operator with potential in the parabolic Kato class on a cylindrical domain Ω. We apply these estimates to obtain a new and shorter proof of the Harnack inequality [16], and to study the boundary behavior of nonnegative solutions.
Estimates of -harmonic conjugate operator.
Estimates of the potential kernel and Harnack's inequality for the anisotropic fractional Laplacian
We characterize those homogeneous translation invariant symmetric non-local operators with positive maximum principle whose harmonic functions satisfy Harnack's inequality. We also estimate the corresponding semigroup and the potential kernel.
Estimation of Green's function on piecewise Dini-smooth bounded Jordan domains
We establish inequalities for Green functions on general bounded piecewise Dini-smooth Jordan domains in ℝ². This enables us to prove a new version of the 3G Theorem which generalizes its previous version given in [M. Selmi, Potential Anal. 13 (2000)]. Using these results, we give a comparison theorem for the Green kernel of Δ and the Green kernel of Δ - μ, where μ is a nonnegative and exact Radon measure.
Estimées à poids de l’opérateur de Green sur une variété de Stein
Evolutionary equation of inertial waves in 3-D multiply connected domain with Dirichlet boundary condition.
Exact solutions to some external mixed problems in potential theory
A new and elegant procedure is proposed for the solution of mixed potential problems in a half-space with a circular line of division of boundary conditions. The approach is based on a new type of integral operators with special properties. Two general external problems are solved; i) An arbitrary potential is specified at the boundary outside a circle, and its normal derivative is zero inside; ii) An arbitrary normal derivative is given outside the circle, and be potential is zero inside. Several...
Exactness of the approximation of subharmonic function by the logarithm of the modulus of an analytic function in the Chebyshev metric.
Exakte Größenordnung für das Randverhalten des Poissonschen Integrals von BMO-Funktionen und VMO-Funktionen
Examples in the Classification Theory of Riemannian Manifolds and the Equation ...u = Pu.
Examples of non-local time dependent or parabolic Dirichlet spaces
In [23] M. Pierre introduced parabolic Dirichlet spaces. Such spaces are obtained by considering certain families of Dirichlet forms. He developed a rather far-reaching and general potential theory for these spaces. In particular, he introduced associated capacities and investigated the notion of related quasi-continuous functions. However, the only examples given by M. Pierre in [23] (see also [22]) are Dirichlet forms arising from strongly parabolic differential operators of second order. To...
Exceptional Sets and Harmonie Morphisms.
Exceptional Sets in a Product of Harmonie Spaces.
Existence and geometric properties of solutions of a free boundary problem in potential theory.