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The boundary-value problems for Laplace equation and domains with nonsmooth boundary

Dagmar Medková (1998)

Archivum Mathematicum

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 evolution and Poisson kernels on nilpotent meta-abelian groups

Richard Penney, Roman Urban (2013)

Studia Mathematica

Let S be a semidirect product S = N⋊ A where N is a connected and simply connected, non-abelian, nilpotent meta-abelian Lie group and A is isomorphic to k , k>1. We consider a class of second order left-invariant differential operators on S of the form α = L a + Δ α , where α k , and for each a k , L a is left-invariant second order differential operator on N and Δ α = Δ - α , , where Δ is the usual Laplacian on k . Using some probabilistic techniques (e.g., skew-product formulas for diffusions on S and N respectively) we obtain an...

The Pluripolar Hull and the Fine Topology

Armen Edigarian (2005)

Bulletin of the Polish Academy of Sciences. Mathematics

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.

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