Authors: Schweizer, Ben Title: Existence results for the Helmholtz equation in periodic wave-guides with energy methods Language (ISO): en Abstract: The Helmholtz equation $- \nabla \cdot (a \nabla u) - \omega^2 u = f$ is considered in an unbounded wave-guide $\Omega := \mathbb{R} \times S \subset \mathbb{R}^d$, where $S \subset \mathbb{R}^{d-1}$ is a bounded domain. The coefficient $a$ is strictly elliptic and (locally) periodic in the unbounded direction $x_1\in \mathbb{R}$. For non-singular frequencies $\omega$, we show the existence of a solution $u$. While previous proofs of such results were based on operator theory, our proof uses only energy methods. Subject Headings: Helmholtz equationwave-guideperiodic mediaFredholm alternative URI: http://hdl.handle.net/2003/38161http://dx.doi.org/10.17877/DE290R-20140 Issue Date: 2019-05-10 Appears in Collections: Schweizer, Ben Prof. Dr.Preprints der Fakultät für Mathematik

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