$C^{1,\alpha}$ regularity for quasilinear parabolic equations with nonstandard growth
| Autor: | Adimurthi, Karthik, Ghosh, Suchandan, Tewary, Vivek |
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| Rok vydání: | 2022 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | In this paper, we obtain $C^{1,\alpha}$ estimates for weak solutions of certain quasilinear parabolic equations satisfying nonstandard growth conditions, the prototype examples being $$u_t - \text{div} (|\nabla u|^{p-2} \nabla u + a(t)|\nabla u|^{q-2} \nabla u) = 0,$$ $$u_t - \text{div} (|\nabla u|^{p(t)-2} \nabla u) = 0.$$ under the assumption that the solutions a priori have bounded gradient. We build on the recently developed scaling and covering argument which allows us to consider the singular and degenerate cases in a uniform manner and with minimal regularity requirements on the phase switching factor $a(t)$ and the variable exponent $p(t)$. Moreover, we are able to take any $p \leq q < \infty$ to obtain the desired regularity. Comment: 22 pages. arXiv admin note: substantial text overlap with arXiv:2009.02227. Bibliography updated |
| Databáze: | arXiv |
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