Dirichlet-transmission problems for pseudodifferential Brinkman operators on Sobolev and Besov spaces associated to Lipschitz domains in Riemannian manifolds

Potential Theory on Lipschitz Domains in

Potential Theory on Lipschitz Domains in Riemannian Manifolds: Sobolev–Besov Space Results and the Poisson Problem

✍ Marius Mitrea; Michael Taylor 📂 Article 📅 2000 🏛 Elsevier Science 🌐 English ⚖ 450 KB

We continue a program to develop layer potential techniques for PDE on Lipschitz domains in Riemannian manifolds. Building on L p and Hardy space estimates established in previous papers, here we establish Sobolev and Besov space estimates on solutions to the Dirichlet and Neumann problems for the L