Glasnik Matematicki, Vol. 52, No. 1 (2017), 107-113.

A REMARK ON GLOBAL W1,P BOUNDS FOR HARMONIC FUNCTIONS WITH LIPSCHITZ BOUNDARY VALUES

Nikos Katzourakis

Department of Mathematics and Statistics, University of Reading, Whiteknights, PO Box 220, Reading RG6 6AX, United Kindgom
e-mail: n.katzourakis@reading.ac.uk

Abstract.   In this note we show that gradient of harmonic functions on a smooth domain with Lipschitz boundary values is pointwise bounded by a universal function which is in Lp for all finite p≥ 1.

2010 Mathematics Subject Classification.   31B05, 31B20, 31B25, 35B99.

Key words and phrases.   Harmonic functions, Dirichlet problem, Schauder estimates.

Full text (PDF) (free access)

DOI: 10.3336/gm.52.1.08

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