Local Hölder continuity of weak solutions for an anisotropic elliptic equation

摘要

We prove, following DiBenedetto’s intrinsic scaling method, that a local bounded weak solution of the equation $$-sum_{i=1}^{N}frac{partial}{partial x_i}left[left| frac{partial u}{partial x_i} right|^{p_{i}-2} frac{partial u}{partial x_i} right]=f $$in Ω, is locally Hölder continuous, where f is a given bounded function and p i  ≥ 2, for any i = 1, . . . , N. Mathematics Subject Classification Primary 35J60 35J70 35B65 Secondary 35B45 35D30 Keywords Anisotropic elliptic problems Local Hölder continuity Intrinsic scaling method Research supported by CMUC/FCT and by ERC Grant 207573 “Vectorial problems”.