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arXiv · 1612.00950

A limiting absorption principle for the Helmholtz equation with variable coefficients

Federico Cacciafesta·Piero D'Ancona·Renato Lucà
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Abstract

We prove a limiting absorption principle for a generalized Helmholtz equation on an exterior domain with Dirichlet boundary conditions \begin{equation*} (L+λ)v=f, \qquad λ\in \mathbb{R} \end{equation*} under a Sommerfeld radiation condition at infinity. The operator $L$ is a second order elliptic operator with variable coefficients, the principal part is a small, long range perturbation of $-Δ$, while lower order terms can be singular and large. The main tool is a sharp uniform resolvent estimate, which has independent applications to the problem of embedded eigenvalues and to smoothing estimates for dispersive equations.

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Federico Cacciafesta, Piero D'Ancona, Renato Lucà. 2018-01-18. A limiting absorption principle for the Helmholtz equation with variable coefficients. https://arxiv.org/abs/1612.00950

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