Noncoercive Problems Research Articles

On existence of solutions for a class of fully nonlinear noncoercive problems

0) arises in the three- dimensional water wave theory (see M. Shinbrot [lo]), and also in the engineering problem of “hydraulic fracturing” of oil wells, see J. R. Canon and G. H. Meyer [2,7]. Mathematically, the model problem (1) is of interest, since it represents one of the simplest noncoercive elliptic problems (i.e., the Lopatinski-Shapiro condition fails, see [4]) for which there is no general theory. The field of fully nonlinear elliptic equations has recently attracted a great deal of attention (see, e.g., a recent paper of G. M. Lieberman and N. S. Trudinger [6] and the references therein to other work of the same authors as well as that of L. Evans, N. Krylov, P. L. Lions, and others). It appears that the case of second order boundary operators is not well studied, particularly for noncoercive problems. We present an existence result for (l), which extends the one in [3], where we had considered the equation

Existence of solutions for a class of semilinear noncoercive problems

Existence of solutions for a class of semilinear noncoercive problems

Existence of solutions for a class of nonlinear non-coercive problems

(1983). Existence of solutions for a class of nonlinear non-coercive problems. Communications in Partial Differential Equations: Vol. 8, No. 8, pp. 819-846.

On pseudo-monotone operators and nonlinear noncoercive variational problems on unbounded domains

On pseudo-monotone operators and nonlinear noncoercive variational problems on unbounded domains

Generalized projection theorem and weak noncoercive evolution problems in Hilbert space

Generalized projection theorem and weak noncoercive evolution problems in Hilbert space

Solutions of some possibly noncoercive evolution problems with regular data

We consider some weak first order evolution equations with variable domains of the form (1.1). A framework is presented wherein regularity of the data /and u0 is systematically inserted into the formulation of the existence problem and a general abstract existence theorem is proved. It is shown that this theorem applies to a wide class of concrete noncoercive problems and gives new results even for constant domain problems.