The Bloch Space of M-Harmonic Functions on Bounded Symmetric Domains.
The boundary Harnack principle for the fractional Laplacian
We study nonnegative functions which are harmonic on a Lipschitz domain with respect to symmetric stable processes. We prove that if two such functions vanish continuously outside the domain near a part of its boundary, then their ratio is bounded near this part of the boundary.
The boundary value problem for Dirac-harmonic maps
Dirac-harmonic maps are a mathematical version (with commuting variables only) of the solutions of the field equations of the non-linear supersymmetric sigma model of quantum field theory. We explain this structure, including the appropriate boundary conditions, in a geometric framework. The main results of our paper are concerned with the analytic regularity theory of such Dirac-harmonic maps. We study Dirac-harmonic maps from a Riemannian surface to an arbitrary compact Riemannian manifold. We...
The boundary-value problems for Laplace equation and domains with nonsmooth boundary
Dirichlet, Neumann and Robin problem for the Laplace equation is investigated on the open set with holes and nonsmooth boundary. The solutions are looked for in the form of a double layer potential and a single layer potential. The measure, the potential of which is a solution of the boundary-value problem, is constructed.
The Bremermann-Dirichlet problem for -plurisubharmonic functions
The Brothers Riesz theorem in and Laplace series.
The Cauchy transform of continuous linear functionals and projections on the weighted spaces of analytic functions.
The classification problem for the capacities associated with the Besov and Triebel-Lizorkin spaces
The complex Monge-Ampère operator in hyperconvex domains
The Convergence of Even Degree Spline Collocation Solution for Potential Problems in Smooth Domains of the Plane.
The converse of the Fatou theorem for smooth measures.
The current situation in the linear problem of Molodenskii
Si prova l'esistenza di un'unica soluzione debole che dipende con continuità dai dati al contorno per il problema lineare di Molodenskii in approssimazione quasi sferica, nel caso che la superficie al contorno soddisfi una condizione di cono. Si segue un approccio costruttivo diretto, che generalizza una procedura precedentemente elaborata per il problema semplice di Molodenskii. Inoltre si prova che la soluzione ha derivate prime a quadrato integrabile al contorno, il che è essenziale per le applicazioni...
The Definition of Energy in Non-Symmetric Translation Invariant Dirichlet Spaces.
The density of the area integral in
Let be a harmonic function in the half-plane , . We define a family of functionals , that are analogs of the family of local times associated to the process where is Brownian motion in . We show that is bounded in if and only if belongs to , an equivalence already proved by Barlow and Yor for the supremum of the local times. Our proof relies on the theory of singular integrals due to Caldéron and Zygmund, rather than the stochastic calculus.
The Dirchlet Problem for a Complex Monge-Ampère Equation.
The Dirichlet problem for harmonic functions with boundary values from Zygmund classes.
The Dirichlet problem for harmonic maps from the disk into the euclidean n-sphere
The Dirichlet Problem for Sublaplacians on Nilpotent Gruops - Geometric Criteria For Regularity.
The Dirichlet problem for the biharmonic equation in a Lipschitz domain
The Dirichlet problem for the biharmonic equation in a Lipschitz domain
In this paper we study and give optimal estimates for the Dirichlet problem for the biharmonic operator , on an arbitrary bounded Lipschitz domain in . We establish existence and uniqueness results when the boundary values have first derivatives in , and the normal derivative is in . The resulting solution takes the boundary values in the sense of non-tangential convergence, and the non-tangential maximal function of is shown to be in .