We consider a bounded open subset Ω of Rⁿ of class C1,α for some α ∈ ]0,1[ and we solve the Neumann problem for the Helmholtz equation both in Ω and in the exterior of Ω . We look for solutions in the space of α -Hölder continuous functions that may not have a classical normal derivative at the boundary points of Ω and that may have an infinite Dirichlet integral around the boundary of Ω . Namely for solutions that do not belong to the classical variational setting.
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Massimo Lanza de Cristoforis (2025) studied this question.
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