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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

MSC:
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
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