Finite-Dimensional Approximations of the Steklov–Poincaré Operator for the Helmholtz Equation in Periodic Waveguides
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DOI: 10.1007/s10958-018-3890-1
Abstract: We consider the Dirichlet and Neumann problems for the Laplace operator in periodic waveguides. Integro-differential connections between the solution and its normal derivative, interpreted as a finite-dimensional version of the Steklov–Poincaré operator, are imposed on… read more here.
Keywords: steklov poincar; finite dimensional; poincar operator; periodic waveguides ... See more keywords
A Remark on the Steklov–Poincaré Inequality
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DOI: 10.1134/s0001434621070233
Abstract: In an $$n$$ -dimensional bounded domain $$\Omega_n$$ , $$n\ge 2$$ , we prove the Steklov–Poincare inequality with the best constant in the case where $$\Omega_n$$ is an $$n$$ -dimensional ball. We also consider the case… read more here.
Keywords: steklov poincar; remark steklov; steklov; inequality ... See more keywords