We consider a bounded open subset of of class for some and we solve the Neumann problem for the Helmholtz equation both in and in the exterior of. We look for solutions in the space of Holder continuous functions that may not have a classical normal derivative at the boundary points of and that may have an infinite Dirichlet integral around the boundary of. Namely for solutions that do not belong to the classical variational setting.
A nonvariational Neumann problem for the Helmholtz equation
Lanza de Cristoforis, Massimo
2025
Abstract
We consider a bounded open subset of of class for some and we solve the Neumann problem for the Helmholtz equation both in and in the exterior of. We look for solutions in the space of Holder continuous functions that may not have a classical normal derivative at the boundary points of and that may have an infinite Dirichlet integral around the boundary of. Namely for solutions that do not belong to the classical variational setting.
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