Existence and Multiplicity for Elliptic Problems with Quadratic Growth in the Gradient

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.     

Existence conditions for non-safe loads in masonry-like bodies

We study the existence of minimizers for a class of noncoercive functionals, representing the strain energy of masonry-like bodies subject to loads that are not “safe” with respect to certain existence conditions estblished in the literature. Some more general sufficient conditions for existence are proved, and two simple noncoercive examples are discussed making use of these conditions.