Displaying similar documents to “Invariance of the Fredholm radius of the Neumann operator”

On essential norm of the Neumann operator

Dagmar Medková (1992)

Mathematica Bohemica

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One of the classical methods of solving the Dirichlet problem and the Neumann problem in 𝐑 m is the method of integral equations. If we wish to use the Fredholm-Radon theory to solve the problem, it is useful to estimate the essential norm of the Neumann operator with respect to a norm on the space of continuous functions on the boundary of the domain investigated, where this norm is equivalent to the maximum norm. It is shown in the paper that under a deformation of the domain investigated...

The third boundary value problem in potential theory for domains with a piecewise smooth boundary

Dagmar Medková (1997)

Czechoslovak Mathematical Journal

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The paper investigates the third boundary value problem ∂ u ∂ n + λ u = μ for the Laplace equation by the means of the potential theory. The solution is sought in the form of the Newtonian potential (1), (2), where ν is the unknown signed measure on the boundary. The boundary condition (4) is weakly characterized by a signed measure T ν . Denote by T ν → T ν the corresponding operator on the space of signed measures on the boundary of the investigated domain G . If there is α ≠ 0 such that the essential spectral radius...