Abstract
We establish the L2 -solvability of Dirichlet, Neumann and regularity problems for divergence-form heat (or diffusion) equations with time-independent Hölder-continuous diffusion coefficients on bounded Lipschitz domains in ℝn. This is achieved through the demonstration of invertibility of the relevant layer potentials, which is in turn based on Fredholm theory and a systematic transference scheme which yields suitable parabolic Rellich-type estimates.
Original language | English |
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Pages (from-to) | 265-319 |
Number of pages | 55 |
Journal | Transactions of the American Mathematical Society |
Volume | 370 |
Issue number | 1 |
DOIs | |
Publication status | Published - Jan 1 2018 |
Keywords
- Boundary value problems
- Layer potentials
- Lipschitz domains
- Parabolic equations
- Rellich estimates
ASJC Scopus subject areas
- Mathematics(all)
- Applied Mathematics