Work

A nonvariational Neumann problem for the Helmholtz equation

Year: 2025

Type: article

Abstract: We consider a bounded open subset $$\Omega $$ of $${\mathbb {R}}^n$$ of class $$C^{1,\alpha }$$ for some $$\alpha \in ]0,1[$$ and we solve the Neumann problem for the Helmholtz equation both in $$\Omega $$ and in the exterior of $$\Omega $$ . We look for solutions in the space of $$\alpha $$ -Hölder continuous functions that may not have a classical normal derivative at the boundary points of $$\Omega $$ and that may have an infinite Dirichlet integral around the boundary of $$\Omega $$ . Namely for solutions that do not belong to the classical variational setting.

Source: Annali di Matematica Pura ed Applicata (1923 -)

DOI: 10.1007/s10231-025-01614-8

Author: Massimo Lanza de Cristoforis

Institution: University of Padua

Language: English

Topic: Differential Equations and Boundary Problems

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,190

Funders: Istituto Nazionale di Alta Matematica "Francesco Severi", European Commission, Ministero dell’Istruzione, dell’Università e della Ricerca, Horizon 2020 Framework Programme