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Oblique derivative problem for quasilinear elliptic equations with VMO coefficients

Published online by Cambridge University Press:  17 April 2009

Guiseppe Di Fazio  and
Dian K. Palagachev
Guiseppe Di Fazio
Affiliation:
Department of MathematicsUniversity of CataniaViale A. Doria 695125 CataniaItaly e-mail-DiFazio@dipmat.unict.it
Dian K. Palagachev
Affiliation:
Department of MathematicsTechnological University of Sofia8 “Kl. Okhridski” blvSofia - 1756Bulgaria e-mail: dian@bgcict.acad.bg
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Abstract

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Strong solvability and uniqueness in the Sobolev space W2, q(Ω), q > n, are proved for the oblique derivative problem

assuming the coefficients of the quasilinear elliptic operator to be Carathéodory functions, aij ∈ VMO∩L∞ with respect to x, and b to grow at most quadratically with respect to the gradient.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 53 , Issue 3 , June 1996 , pp. 501 - 513
Copyright
Copyright © Australian Mathematical Society 1996

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