2025/04/15 by de Cristoforis, M. Lanza
#31B10 #35J05 #35J25 #Analysis of PDEs (math.AP) #FOS: Mathematics
paper · doi:10.48550/arxiv.2504.12349
We consider a bounded open subset Ω of ℝn of class C1,α for some α∈]0,1[ and the space V-1,α(∂Ω) of (distributional) normal derivatives on the boundary of α-Hölder continuous functions in Ω that have Laplace operator in the Schauder space with negative exponent C-1,α(Ω). Then we prove those properties of the acoustic single layer potential that are necessary to analyze the Neumann problem for the Helmholtz equation in Ω with boundary data in V-1,α(∂Ω) and solutions in the space of α-Hölder continuous functions in Ω that have Laplace operator in C-1,α(Ω), i.e., in a space of functions that may have infinite Dirichlet integral. Namely, a Neumann problem that does not belong to the classical variational setting.