The insertion of regular sets in potential theory
The integral equation methods for the perturbed Helmholtz eigenvalue problems.
The Intersection of the Closures of Two Disjoint Strongly Pseudoconvex Domains.
The inverse problem for elliptic equations from Dirichlet to Neumann map in multiply connected domains.
The Lévy laplacian and differential operators of 2-nd order in Hilbert spaces
We shall show that every differential operator of 2-nd order in a real separable Hilbert space can be decomposed into a regular and an irregular operator. Then we shall characterize irregular operators and differential operators satisfying the maximum principle. Results obtained for the Lévy laplacian in [3] will be generalized for irregular differential operators satisfying the maximum principle.
The logarithmic capacity in
The Lusin-Menchoff property of fine topologies
The Martin Boundary for Harmonic Functions on Groups of Automorphisms of a Homogeneous Tree.
The Martin compactification of a plane domain
We prove that the Martin compactification of a plane domain is homeomorphic to a subset of the two-dimensional sphere.
The Martin compactification of the Cartesian product of two hyperbolic spaces.
The Martin compactification of the polydisc at the bottom of the positive spectrum.
The Max-Plus Martin boundary.
The mean curvature measure
We assign a measure to an upper semicontinuous function which is subharmonic with respect to the mean curvature operator, so that it agrees with the mean curvature of its graph when the function is smooth. We prove that the measure is weakly continuous with respect to almost everywhere convergence. We also establish a sharp Harnack inequality for the minimal surface equation, which is crucial for our proof of the weak continuity. As an application we prove the existence of weak solutions to the...
The Method of Lines for Poisson's Equation with Nonlinear or Free Boundary Conditions.
The minimum modulus of a subharmonic function
The multiple layer potential for the biharmonic equation in variables
The definition of multiple layer potential for the biharmonic equation in is given. In order to represent the solution of Dirichlet problem by means of such a potential, a singular integral system, whose symbol determinant identically vanishes, is considered. The concept of bilateral reduction is introduced and employed for investigating such a system.
The Neumann problem for the 2-D Helmholtz equation in a domain, bounded by closed and open curves.
The Neumann problem for the Laplace equation on general domains
The solution of the weak Neumann problem for the Laplace equation with a distribution as a boundary condition is studied on a general open set in the Euclidean space. It is shown that the solution of the problem is the sum of a constant and the Newtonian potential corresponding to a distribution with finite energy supported on . If we look for a solution of the problem in this form we get a bounded linear operator. Under mild assumptions on a necessary and sufficient condition for the solvability...
The obstacle problem for the biharmonic operator
The Partial Legendre Transformation for Plurisubharmonic Functions.