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Journal of the London Mathematical Society 2005 71(2):415-437; doi:10.1112/S0024610704006143
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© The London Mathematical Society

Convergent Rates for Solutions of Dirichlet Problems of Quasilinear Equations

Zhiren Jin and Kirk Lancaster

Department of Mathematics and Statistics, Wichita State University Wichita, KS 67260, USA zhiren{at}math.wichita.edu, lancaster{at}math.wichita.edu

Received 16 February 2003. Revision received 21 July 2004.

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.


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