This paper deals with the questions of the existence and uniqueness of a solution to the Dirichlet problem associated with the Dunkl Laplacian as well as the hypoellipticity of on noninvariant open sets.
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 .
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...
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.
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.
We characterize the Hunt convolution kernels on () whose the Green type kernels on ; ,
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.