Analysis in weighted spaces
Functional calculus and parabolic boundary value problems
F.B. Roodenburg (TU Delft - Electrical Engineering, Mathematics and Computer Science)
M.C. Veraar – Promotor (TU Delft - Electrical Engineering, Mathematics and Computer Science)
E. Lorist – Copromotor (TU Delft - Electrical Engineering, Mathematics and Computer Science)
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Abstract
In this dissertation, we investigate well-posedness and maximal regularity of boundary value problems on rough domains and with singular data. To this end, the problems are formulated in the setting of weighted Sobolev spaces, where the weights are powers of the distance to the boundary. We develop the necessary mathematical framework to treat boundary value problems in this weighted setting, including the theoretical study of weighted function spaces, the abstract operator-theoretic study of the Laplace operator, and the application of these tools to prototype boundary value problems.