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Weighted Calderón-Zygmund estimates for weak solutions of quasi-linear degenerate elliptic equations. (English) Zbl 1435.35174

The paper is devoted to interior and global weighted regularity estimates for weak solutions of non-homogeneous boundary value problems associated to degenerate and singular quasi-linear elliptic equations.
In case of linear equations the regularity results can be considered as the Sobolev counterpart of the Hölder regularity estimates contained in the celebrated paper [E. B. Fabes et al., Commun. Partial Differ. Equations 7, 77–116 (1982; Zbl 0498.35042)].
The author considers Reifenberg flat domains. He points out that neither boundedness nor continuity of the weak solution is assumed.
The author usesa perturbation technique with double-scaling parameter to overcome the difficulty due to the scaling properties of the equations.

MSC:

35J70 Degenerate elliptic equations
35J75 Singular elliptic equations
35J62 Quasilinear elliptic equations
35B45 A priori estimates in context of PDEs

Citations:

Zbl 0498.35042
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Full Text: DOI arXiv

References:

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