Title
Elliptic and Parabolic Problems in NonSmooth Domains,Used
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Regularity of solutions is an important part of the theory of partial differential equations. In this text, the regularity of solutions to elliptic and parabolic problems in Lipschitz domains is investigated. Maximal regularity estimates are useful when dealing with nonlinear parabolic problems. However, the known maximal regularity results for smooth domains no longer hold in Lpspaces over Lipschitz domains for the whole range of exponents p. Here, maximal regularity estimates are shown for the Laplacian with suitable domain in Lpspaces for a restricted range of p. Operators with Lcoefficients in convex domains and OrnsteinUhlenbeck operators in exterior Lipschitz domains are also discussed.
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