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Local regularity of weak solutions of semilinear parabolic systems with critical growth ∗
| Content Provider | Semantic Scholar |
|---|---|
| Author | Berchio, Elvise |
| Copyright Year | 2006 |
| Abstract | We show that, under so called controllable growth conditions, any weak solution in the energy class of the semilinear parabolic system ut(t, x) +Au(t, x) = f(t, x, u, . . . ,∇u), (t, x) ∈ (0, T )× Ω, is locally regular. Here, A is an elliptic matrix differential operator of order 2m. The result is proved by writing the system as a system with linear growth in u, . . . ,∇mu but with “bad” coefficients and by means of a continuity method, where the time serves as parameter of continuity. We also give a partial generalization of previous work of the second author and von Wahl to Navier boundary conditions. Subject–Classification: 35D10, 35K50. |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | http://www-ian.math.uni-magdeburg.de/home/grunau/papers/BerchioGrunau.pdf |
| Language | English |
| Access Restriction | Open |
| Subject Keyword | Coefficient Commutation theorem Emoticon Generalization (Psychology) Linear function Navier–Stokes equations Parabolic antenna Population Parameter Scott continuity Semilinear response Solutions |
| Content Type | Text |
| Resource Type | Article |
