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CONVERGENT RATES FOR SOLUTIONS OF DIRICHLET PROBLEMS OF QUASILINEAR EQUATIONS

Published online by Cambridge University Press:  06 April 2005

ZHIREN JIN  and
KIRK LANCASTER
ZHIREN JIN
Affiliation:
Department of Mathematics and Statistics, Wichita State University, Wichita, KS 67260, USAzhiren@math.wichita.edu, lancaster@math.wichita.edu
KIRK LANCASTER
Affiliation:
Department of Mathematics and Statistics, Wichita State University, Wichita, KS 67260, USAzhiren@math.wichita.edu, lancaster@math.wichita.edu
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Abstract

The convergent rates for bounded solutions of Dirichlet problems of quasilinear elliptic (possibly degenerate) equations in slab-like domains are derived in terms of the convergent rates of the boundary data and the coefficients of the operator. The equations considered include the prescribed mean curvature equation. The results are proved by constructing a family of local barrier functions based on the structure of the operator and the convergent rate of the boundary data. The construction of local barriers is inspired by early work due to Finn and Serrin that is related to the minimal surface equation.

Keywords

35J2535J6035J70
Type
Notes and Papers
Information
Journal of the London Mathematical Society , Volume 71 , Issue 2 , April 2005 , pp. 415 - 437
Copyright
The London Mathematical Society 2005

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