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Solution of elliptic problem with not fully specified Dirichlet boundary value conditions and its application in hydrodynamics

Miloslav Feistauer (1979)

Aplikace matematiky

The author solves a mixed boundary value problem for linear partial differential equations of the elliptic type in a multiply connected domain. Dirichlet conditions are given on the components of the boundary of the domain up to some additive constants which are not known a priori. These constants are to be determined, together with the solution of the boundary value problem, to fulfil some additional conditions. The results are immediately applicable in hydrodynamics to the solution of problems...

Solution of the Dirichlet problem for the Laplace equation

Dagmar Medková (1999)

Applications of Mathematics

For open sets with a piecewise smooth boundary it is shown that a solution of the Dirichlet problem for the Laplace equation can be expressed in the form of the sum of the single layer potential and the double layer potential with the same density, where this density is given by a concrete series.

Solution of the Neumann problem for the Laplace equation

Dagmar Medková (1998)

Czechoslovak Mathematical Journal

For fairly general open sets it is shown that we can express a solution of the Neumann problem for the Laplace equation in the form of a single layer potential of a signed measure which is given by a concrete series. If the open set is simply connected and bounded then the solution of the Dirichlet problem is the double layer potential with a density given by a similar series.

Solution of the Robin problem for the Laplace equation

Dagmar Medková (1998)

Applications of Mathematics

For open sets with a piecewise smooth boundary it is shown that we can express a solution of the Robin problem for the Laplace equation in the form of a single layer potential of a signed measure which is given by a concrete series.

Soluzioni di viscosità

Italo Capuzzo Dolcetta (2001)

Bollettino dell'Unione Matematica Italiana

This is the expanded text of a lecture about viscosity solutions of degenerate elliptic equations delivered at the XVI Congresso UMI. The aim of the paper is to review some fundamental results of the theory as developed in the last twenty years and to point out some of its recent developments and applications.

Solvability of the Poisson equation in weighted Sobolev spaces

Wojciech M. Zajączkowski (2010)

Applicationes Mathematicae

The aim of this paper is to prove the existence of solutions to the Poisson equation in weighted Sobolev spaces, where the weight is the distance to some distinguished axis, raised to a negative power. Therefore we are looking for solutions which vanish sufficiently fast near the axis. Such a result is useful in the proof of the existence of global regular solutions to the Navier-Stokes equations which are close to axially symmetric solutions.

Some Dirichlet spaces obtained by subordinate reflected diffusions.

Niels Jacob, René L. Schilling (1999)

Revista Matemática Iberoamericana

In this paper we want to show how well-known results from the theory of (regular) elliptic boundary value problems, function spaces and interpolation, subordination in the sense of Bochner and Dirichlet forms can be combined and how one can thus get some new aspects in each of these fields.

Some fast finite-difference solvers for Dirichlet problems on general domains

Ta Van Dinh (1982)

Aplikace matematiky

The author proves the existence of the multi-parameter asymptotic error expansion to the five-point difference scheme for Dirichlet problems for the linear and semilinear elliptic PDE on general domains. By Richardson extrapolation, this expansion leads to a simple process for accelerating the convergence of the method.

Some fast finite-difference solvers for Dirichlet problems on special domains

Ta Van Dinh (1982)

Aplikace matematiky

The author proves the existence of the multi-parameter asymptotic error expansion to the usual five-point difference scheme for Dirichlet problems for the linear and semilinear elliptic PDE on the so-called uniform and nearly uniform domains. This expansion leads, by Richardson extrapolation, to a simple process for accelerating the convergence of the method. A numerical example is given.

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