# Higher-Order Regularity for the Solutions of Some Degenerate Quasilinear Elliptic Equations in the Plane

Liu, Wenbin, Barrett, John W. (1993) Higher-Order Regularity for the Solutions of Some Degenerate Quasilinear Elliptic Equations in the Plane. SIAM Journal on Mathematical Analysis, 24 (6). pp. 1522-1536. ISSN 0036-1410. (doi:10.1137/0524086) (The full text of this publication is not currently available from this repository. You may be able to access a copy if URLs are provided) (KAR id:37140)

 The full text of this publication is not currently available from this repository. You may be able to access a copy if URLs are provided. (Contact us about this Publication) Official URLhttp://dx.doi.org/10.1137/0524086

## Abstract

Local $C^{k,\beta }$ and $W^{2 + k,v}$ ($k \geq 1,\beta > 0$, and $v \geq 1$) regularity is established for the solutions of a class of degenerate quasilinear elliptic equations, which include the p-Laplacian. Unlike the known local regularity results for such equations, k is larger than 2 in many notable cases. These results generalize those in [13], which were established only for the p-Laplacian. Furthermore, local results are extended to obtain a global regularity result in some cases. Global results of this type are essential in proving optimal error bounds for the finite element approximation of such equations.

Item Type: Article 10.1137/0524086 Q Science > QA Mathematics (inc Computing science) Divisions > Kent Business School - Division > Kent Business School (do not use) Steve Liu 11 Dec 2013 09:53 UTC 16 Feb 2021 12:50 UTC https://kar.kent.ac.uk/id/eprint/37140 (The current URI for this page, for reference purposes) https://orcid.org/0000-0001-5966-6235