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Some applications of reverse Hölder inequalities with a boundary integral

Research paper by A. A. Arkhipova

Indexed on: 01 Dec '94Published on: 01 Dec '94Published in: Journal of Mathematical Sciences



Abstract

We obtain an increase in the exponent of integrability of the derivatives of solutions of two classes of boundary-value problems. We derive estimates of the corresponding norms of the solutions. For a class of quasilinear elliptic systems we establish an Lp-estimate of the gradient of the solutions of class Wm1,m > 1, p > m, of a boundary-value problem with nonzero condition on the conormal derivative. To solve Signorini's problem we obtain an Lp-estimate, p > 2,of the second derivatives of an L2-solution with a nonzero one-sided restriction on the conormal derivative. The proof of both results is based on the application of an reverse Hölder inequality with a surface integral established earlier by the author. Bibliography: 5 titles.