Schauder estimate for solutions of Poisson's equation with Neumann boundary condition

By Giacomo Nardi. 2013

60 citations recorded by the source corpus.

In this work we consider the Neumann problem for the Laplace operator and we prove an existence result in the H\"older spaces and obtain Schauder estimates. According to our knowledge this result is not explicitly proved in the several works devoted to the Schauder theory, where similar theorems are proved in detail for the Dirichlet and oblique derivative problems. Our contribution is to make explicit the existence and the estimate for the Neumann problem.

Subfields: Applied Mathematics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/c46895482a62f6a522b08c6cf53c67c5c2fff0b2

Citations in the corpus

• Sharp isoperimetric inequalities via the ABP method (2013, unknown): “ PH(Ω) = R ∂Ω H ν(x) dS. The constant PH(Ω)/|Ω| has been chosen so that the problem has a unique solution up to an additive constant. Since H|Sn−1 and Ω are smooth, we have that u is smooth in Ω. See [47] for a recent exposition of these classical facts and for a new Schauder estimate for (4.1). Con”