A convergence criterion for elliptic variational inequalities

GARIBOLDI, CLAUDIA; OCHAL, ANNA; SOFONEA, MIRCEA; TARZIA, DOMINGO A.

APPLICABLE ANALYSIS

TAYLOR & FRANCIS LTD

Año: 2024 p. 1 - 21

0003-6811

We consider an elliptic variational inequality with unilateral constraints in a Hilbert space X which, under appropriate assumptions on the data, has a unique solution u. We formulate a convergence criterion to the solution u, i.e. we provide necessary and sufficient conditions on a sequence (Formula presented.) which guarantee the convergence (Formula presented.) in the space X. Then we illustrate the use of this criterion to recover well-known convergence results and well-posedness results in the sense of Tykhonov and Levitin–Polyak. We also provide two applications of our results, in the study of a heat transfer problem and an elastic frictionless contact problem, respectively.