TY - JOUR

T1 - Some applications of reverse Hölder inequalities with a boundary integral

AU - Arkhipova, A. A.

PY - 1994/12/1

Y1 - 1994/12/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=34249764625&partnerID=8YFLogxK

U2 - 10.1007/BF01250425

DO - 10.1007/BF01250425

M3 - Article

AN - SCOPUS:34249764625

VL - 72

SP - 3370

EP - 3378

JO - Journal of Mathematical Sciences

JF - Journal of Mathematical Sciences

SN - 1072-3374

IS - 6

ER -