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Solvability of perturbed elliptic equations with critical growth exponent for the gradient. (English) Zbl 0691.35038
A Dirichlet elliptic boundary value problem is considered in a bounded domain. Under certain assumptions (which are too numerous to state here) it is proved that the boundary value problem is weakly solvable. The approach in this paper does not require a priori regularity of the solution except for a standard bound in a suitable Sobolev space. Related results of Boccardo et al., and Del Vecchio are mentioned.
Reviewer: A.G.Ramm

35J65 Nonlinear boundary value problems for linear elliptic equations
35D05 Existence of generalized solutions of PDE (MSC2000)
46A35 Summability and bases in topological vector spaces
Full Text: DOI
[1] Boccardo, L; Murat, F; Puel, J.P, Existence de solutions non bornées pour certain équations quasi-linéaire, Portugal math., 41, 507-534, (1982) · Zbl 0524.35041
[2] Boccardo, L; Murat, F; Puel, J.P, Résultats d’existence pour certains problèmes élliptiques quasilinéaires, Ann. scuola nom. Pisa, 11, 213-235, (1984) · Zbl 0557.35051
[3] Browder, F.E, Existence theory for boundary value problems for quasilinear elliptic systems with strongly nonlinear lower order terms, (), 269-286, No. 23 · Zbl 0148.13501
[4] Frehse, J, A refinement of Rellich’s theorem, Preprint 664, (1984), SFB 72, Bonn · Zbl 0666.46041
[5] Frehse, J, Existence and perturbation theorems for nonlinear elliptic systems, Preprint 576, (1983), SFB 72, Bonn · Zbl 0528.35036
[6] Gilbarg, L.E; Trudinger, N.S, Elliptic partial differential equations of second order, (1977), Springer-Verlag Heidelberg/New York · Zbl 0361.35003
[7] Ladyzhenskaya, O.A; Ural’rseva, N.N, Linear and quasilinear equations, (1968), Academic Press New York/London, (English translation of the 1st Russian edition 1964) · Zbl 0164.13002
[8] Landes, R, On Galerkin’s method in the existence theory of quasilinear elliptic equations, J. funct. anal., 39, 123-148, (1980) · Zbl 0452.35037
[9] \scT. Del Vecchio, Strongly nonlinear problems with Hamiltonian having natural growth, to appear. · Zbl 0714.35035
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