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Regularity of weak solutions of homogeneous or inhomogeneous quasilinear elliptic equations. (English) Zbl 1171.35057
The authors consider elliptic problems of the form ·𝐀(x,u,u)=B(x,u,u) in Ω, where Ω n is not necessary a bounded domain. The principal part can degenerate, e.g., it is a p-Laplacian with 1<p<n, or in the case inhomogeneous A(x,ξ)=ξ p-2 ξ1 - log 1+ξ ξ for ξ n {0}. They obtain conditions for weak solutions uW 1,p (Ω) to belong to L loc m (Ω), 1m, and to W loc 2,p (Ω). They also deal with radial weak solutions. The proofs are based on the Moser iteration scheme and Nirenberg’s translation method. Further results on the radial case appeared in [P. Pucci and R. Servadei, Ann. Inst. Henri Poincaré, Anal. Non Linéaire 25, No. 3, 505–537 (2008; Zbl 1147.35045)].

35J70Degenerate elliptic equations
35J60Nonlinear elliptic equations
35D10Regularity of generalized solutions of PDE (MSC2000)