Abels, Helmut and Grubb, Gerd (2025) Maximal Lp-regularity for x-dependent fractional heat equations with Dirichlet conditions. MATHEMATISCHE ANNALEN, 391 (3). pp. 3295-3331. ISSN 0025-5831, 1432-1807
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We prove optimal regularity results in L-p-based function spaces in space and time for a large class of linear parabolic equations with a nonlocal elliptic operator in bounded domains with limited smoothness. Here the nonlocal operator is given by a strongly elliptic and even pseudodifferential operator P of order 2a (0 < a < 1) with nonsmooth x-dependent coefficients. This includes the prominent case of the fractional Laplacian (-Delta)(a), as well as elliptic operators (-del & sdot; A(x) del + b(x))(a). The proofs are based on general results on maximal L-p-regularity and its relation to R-boundedness of the resolvent of the associated (elliptic) operator. Finally, we apply these results to show existence of strong solutions locally in time for a class of nonlinear nonlocal parabolic equations, which include a fractional nonlinear diffusion equation and a fractional porous medium equation after a transformation. The nonlinear results are new in the case of domains with boundary; the linear results are so when P is x-dependent nonsymmetric.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | PSEUDODIFFERENTIAL BOUNDARY-PROBLEMS; MU-TRANSMISSION; DOMAINS; SPACES; Primary 35S15; 35R11; Secondary 35K61; 35S16; 47G30; 60G52 |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics > Prof. Dr. Helmut Abels |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 17 Mar 2026 09:31 |
| Last Modified: | 17 Mar 2026 09:31 |
| URI: | https://pred.uni-regensburg.de/id/eprint/64505 |
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