On the Dirichlet Problem at Infinity for Manifolds of Nonpositive Curvature.
On the Dirichlet problem for functions of the first Baire class
Let be a simplicial function space on a metric compact space . Then the Choquet boundary of is an -set if and only if given any bounded Baire-one function on there is an -affine bounded Baire-one function on such that on . This theorem yields an answer to a problem of F. Jellett from [8] in the case of a metrizable set .
On the Dirichlet Problem for the Complex Monge-Ampère Operator.
On the equivalence between locally polar and globally polar sets in
On the equivalence of Green functions for general Schrödinger operators on a half-space
We consider the general Schrödinger operator on a half-space in ℝⁿ, n ≥ 3. We prove that the L-Green function G exists and is comparable to the Laplace-Green function provided that μ is in some class of signed Radon measures. The result extends the one proved on the half-plane in [9] and covers the case of Schrödinger operators with potentials in the Kato class at infinity considered by Zhao and Pinchover. As an application we study the cone of all positive L-solutions continuously vanishing...
On the Existence of a Green Function for Harmonie Spaces.
On the existence of solutions to a fourth-order quasilinear resonant problem.
On the existence of steady-state solutions to the Navier-Stokes system for large fluxes
In this paper we deal with the stationary Navier-Stokes problem in a domain with compact Lipschitz boundary and datum in Lebesgue spaces. We prove existence of a solution for arbitrary values of the fluxes through the connected components of , with possible countable exceptional set, provided is the sum of the gradient of a harmonic function and a sufficiently small field, with zero total flux for bounded.
On the Existence of Sub-Markovian Resolvents.
On the existence of weighted boundary limits of harmonic functions
We study the existence of tangential boundary limits for harmonic functions in a Lipschitz domain, which belong to Orlicz-Sobolev classes. The exceptional sets appearing in this discussion are evaluated by use of Bessel-type capacities as well as Hausdorff measures.
On the extension in the Hardy classes and the Nevanlinna class
On the Fejér-F. Riesz inequality in
On the Gauss map of complete surfaces of constant mean curvature in R3 and R4.
On the Green type kernels on the half space in
We characterize the Hunt convolution kernels on () whose the Green type kernels on ; ,
On the Hardy-Littlewood maximal theorem.
On the Harmonie Continuation of Bounded Harmonie Functions.
On the Hartogs-type series for harmonic functions on Hartogs domains in , m ≥ 2
We study series expansions for harmonic functions analogous to Hartogs series for holomorphic functions. We apply them to study conjugate harmonic functions and the space of square integrable harmonic functions.
On the Hausdorff dimension of harmonic measure in higher dimension.
On the heat potential of the double distribution
On the identity of Keldych solutions