Palagachev, Dian K. Quasilinear divergence form elliptic equations in rough domains. (English) Zbl 1190.35220 Complex Var. Elliptic Equ. 55, No. 5-6, 581-591 (2010). Summary: Existence and global Hölder continuity are proved for the weak solution to the Dirichlet problem \[ \begin{cases} \text{div}(a^{ij}(x,u)D_ju+ a^i(x,u))= b(x,u,Du) &\text{in }\Omega\subset\mathbb R^n,\\ u=0 &\text{on }\partial\Omega,\end{cases} \]over Reifenberg flat domains \(\Omega\). The principal coefficients \(a^{ij}(x,u)\) are discontinuous with respect to \(x\) with small BMO-norms and \(b(x,u,Du)\) grows as \(|Du|^r\) with \(r<1+2/n\). Cited in 3 Documents MSC: 35R05 PDEs with low regular coefficients and/or low regular data 35J62 Quasilinear elliptic equations 35J25 Boundary value problems for second-order elliptic equations 35B45 A priori estimates in context of PDEs 35B65 Smoothness and regularity of solutions to PDEs 35D30 Weak solutions to PDEs Keywords:divergence form quasilinear elliptic equations; weak solvability; Hölder regularity; a priori estimates; Reifenberg flat domain; BMO PDFBibTeX XMLCite \textit{D. K. Palagachev}, Complex Var. Elliptic Equ. 55, No. 5--6, 581--591 (2010; Zbl 1190.35220) Full Text: DOI References: [1] DOI: 10.1002/cpa.20037 · Zbl 1112.35053 · doi:10.1002/cpa.20037 [2] DOI: 10.1007/BF02547186 · Zbl 0099.08503 · doi:10.1007/BF02547186 [3] Toro T, Notices Amer. Math. Soc. 44 pp 1087– (1997) [4] Ladyzhenskaya OA, Linear and Quasilinear Equations of Elliptic Type,, 2. ed. (1973) [5] Gilbarg D, Elliptic Partial Differential Equations of Second Order,, 3. ed. (1997) [6] DOI: 10.2307/2154833 · Zbl 0833.35048 · doi:10.2307/2154833 [7] DOI: 10.1002/3527600868 · doi:10.1002/3527600868 [8] DOI: 10.1007/s00208-006-0014-x · Zbl 1194.35157 · doi:10.1007/s00208-006-0014-x This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.