A~priori estimates and blow-up of solutions to nonlinear partial differential equations and inequalities

E. Mitidieri ; S. I. Pokhozhaev

Trudy Matematicheskogo Instituta imeni V.A. Steklova, A priori estimates and blow-up of solutions to nonlinear partial differential equations and inequalities, Tome 234 (2001), pp. 3-383.

Résumé

A general approach is proposed to a priori estimates for solutions to nonlinear partial differential equations and inequalities. Applications of these estimates to the problem of nonexistence of solutions are considered. The method is based on the concept of nonlinear capacity induced by a nonlinear differential operator. The contents of this volume are divided into three parts devoted to elliptic, parabolic, and hyperbolic nonlinear problems. For specialists in nonlinear partial differential equations, mathematical physics, and applied mathematics, as well as for postgraduates and senior students of relevant specialities.

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