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Global Regularity of Weak Solutions to Quasilinear Elliptic and Parabolic Equations with Controlled Growth |
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| Authors: | Hongjie Dong Doyoon Kim |
| Affiliation: | 1. Division of Applied Mathematics , Brown University , Providence, Rhode Island, USA Hongjie_Dong@brown.edu;3. Department of Applied Mathematics , Kyung Hee University , Yongin-si, Republic of Korea |
| Abstract: | We establish global regularity for weak solutions to quasilinear divergence form elliptic and parabolic equations over Lipschitz domains with controlled growth conditions on low order terms. The leading coefficients belong to the class of BMO functions with small mean oscillations with respect to x. |
| Keywords: | BMO coefficients Boundary value problems Quasilinear elliptic and parabolic equations Sobolev spaces |