Existence and multiplicity for elliptic problems with quadratic growth in the gradient

Abstract

We show that a class of divergence-form elliptic problems with quadratic growth in the gradient and non-coercive zero order terms are solvable, under essentially optimal hypotheses on the coefficients in the equation. In addition, we prove that the solutions are in general not unique. The case where the zero order term has the opposite sign was already intensively studied and the uniqueness is the rule.

To appear in Comm. PDE

References in corpus (1)

• Correlation between two quasilinear elliptic problems with a source term involving the function or its gradient

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