Integral representation and $L^ \infty$ bounds for solutions of the Helmholtz equation on arbitrary open sets in $\mathbb{R}^ 2$ and $\mathbb{R}^ 3$

A priori estimates in context of PDEs (35B45) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Inequalities involving derivatives and differential and integral operators (26D10)

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Integral representation and \(L^ \infty\) bounds for solutions of the Helmholtz equation on arbitrary open sets in \(\mathbb{R}^ 2\) and \(\mathbb{R}^ 3\)