Josef Král

ON THE NEUMANN-POINCARE OPERATOR

AbstractLet Γ be a rectifiable Jordan curve in the finite complex plane

Contractivity of C. Neumann's operator in potential theory

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Potential Theory Surveys and Problems

which is regular in the sense of Ahlfors and David. Denote by LC2(Г) the space of all complex-valued functions on Γ which are square integrable w.r. to the arc-length on Γ. Let L2(Γ) stand for the space of all real-valued functions in LC2(Г) and put

Angular limits of double layer potentials

L_0^2 (\Gamma ) = \{ h \in L^2 (\Gamma );{\text{ }}\int_\Gamma {h(\zeta )|d\zeta | = 0} \}

Some inequalities concerning the cyclic and radial variations of a plane path-curve

Since the Cauchy singular operator is bounded on LC2(Г), the Neumann-Poincaré operator C1Г sending each h ∈ L2(Γ) into