Boundary regularity for quasi-linear elliptic equations with continuous boundary data

Chi ping Lau

doi:10.1080/03605308608820442

Boundary regularity for quasi-linear elliptic equations with continuous boundary data

Chi ping Lau^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › Research › peer-review

Abstract

Suppose G is a bounded C² domain in _ℝⁿ, n ≥2. We examine the regularity at the boundary of solutions to a class of quasi-linear elliptic equations having continuous boundary values φ. If φhas a modulus of continuity ß, we give a modulus of continuity for the solution which depends on ßand the generalized mean curvature of ∂G. When the order of non-uniformity of the equation is between 0 and 1, no curvature condition on ∂G is needed.

Original language	English
Pages (from-to)	713-731
Number of pages	19
Journal	Communications in Partial Differential Equations
Volume	11
Issue number	7
DOIs	https://doi.org/10.1080/03605308608820442
Publication status	Published - 1 Jan 1986
Externally published	Yes

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AB - Suppose G is a bounded C2 domain in ℝn, n ≥2. We examine the regularity at the boundary of solutions to a class of quasi-linear elliptic equations having continuous boundary values φ. If φhas a modulus of continuity ß, we give a modulus of continuity for the solution which depends on ßand the generalized mean curvature of ∂G. When the order of non-uniformity of the equation is between 0 and 1, no curvature condition on ∂G is needed.

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JF - Communications in Partial Differential Equations

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Boundary regularity for quasi-linear elliptic equations with continuous boundary data

Abstract

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