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Convergent Rates for Solutions of Dirichlet Problems of Quasilinear Equations
Author(s) -
Jin Zhiren,
Lancaster Kirk
Publication year - 2005
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/s0024610704006143
Subject(s) - mathematics , bounded function , mathematical analysis , operator (biology) , degenerate energy levels , dirichlet problem , dirichlet distribution , curvature , boundary (topology) , boundary value problem , work (physics) , geometry , physics , biochemistry , chemistry , repressor , quantum mechanics , transcription factor , gene , thermodynamics
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.