Research output: Contribution to journal › Article › peer-review
Some applications of reverse Hölder inequalities with a boundary integral. / Arkhipova, A. A.
In: Journal of Mathematical Sciences, Vol. 72, No. 6, 01.12.1994, p. 3370-3378.Research output: Contribution to journal › Article › peer-review
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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 -
ID: 15546875