Continuous extendibility of solutions of the third problem for the Laplace equation

Dagmar Medková

Displaying similar documents to “Continuous extendibility of solutions of the third problem for the Laplace equation”

Boundedness of the solution of the third problem for the Laplace equation

Dagmar Medková (2005)

Czechoslovak Mathematical Journal

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A necessary and sufficient condition for the boundedness of a solution of the third problem for the Laplace equation is given. As an application a similar result is given for the third problem for the Poisson equation on domains with Lipschitz boundary.

Continuous extendibility of solutions of the Neumann problem for the Laplace equation

Dagmar Medková (2003)

Czechoslovak Mathematical Journal

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A necessary and sufficient condition for the continuous extendibility of a solution of the Neumann problem for the Laplace equation is given.

The Neumann problem for the Laplace equation on general domains

Dagmar Medková (2007)

Czechoslovak Mathematical Journal

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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 $G$ 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 $\partial G$ . If we look for a solution of the problem in this form we get a bounded linear operator. Under mild assumptions on $G$ a necessary and sufficient condition for...