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.
The Pluripolar Hull and the Fine Topology
We show that the projections of the pluripolar hull of the graph of an analytic function in a subdomain of the complex plane are open in the fine topology.
The Poincaré Inequality Does Not Improve with Blow-Up
For each β > 1 we construct a family Fβ of metric measure spaces which is closed under the operation of taking weak-tangents (i.e. blow-ups), and such that each element of Fβ admits a (1, P)-Poincaré inequality if and only if P > β.
The Poisson boundary for rank one manifolds and their compact lattices.
The Poisson Boundary of the Mapping Class Group and of Teichmüller Space
The Poisson formula for groups with hyperbolic properties.
The Poisson integral for a ball in spaces of constant curvature
We present explicit expressions of the Poisson kernels for geodesic balls in the higher dimensional spheres and real hyperbolic spaces. As a consequence, the Dirichlet problem for the projective space is explicitly solved. Comparison of different expressions for the same Poisson kernel lead to interesting identities concerning special functions.
The Poisson Space of the Koranyi Ball.
The Poisson summation formula for a Dirichlet problem with gliding and glancing rays
The Poisson's problem for the Laplacian with Robin boundary condition in non-smooth domains.
The problem and singular integrals on Orlicz spaces