Glasnik Matematicki, Vol. 51, No. 1 (2016), 223-236.

GLOBAL INTEGRABILITY FOR SOLUTIONS TO BOUNDARY VALUE PROBLEMS OF ANISOTROPIC FUNCTIONALS

Gao Hongya, Liang Shuang and Cui Yi

College of Mathematics and Information Science, Hebei University, 071002 Baoding, China
e-mail: ghy@hbu.cn
e-mail: 944204016@qq.com
e-mail: 854304981@qq.com

Abstract.   This paper deals with solutions to boundary value problems of anisotropic integral functionals

I(u) = ∫Ω f(x,Du(x))dx,
with the energy f(x,z) has growth pi with respect to zi, like in
∫Ω ((1+∑j=1n |Dju|pj )(p1-2)/p1 |D1u|2 + ⋯ + (1+∑j=1n |Dju|pj )(pn-2)/pn |Dnu|2) dx.
We show that higher integrability of the boundary datum u* forces minimizers u to be more integrable. A similar result is obtained for obstacle problems.

2010 Mathematics Subject Classification.   49N60, 35J60.

Key words and phrases.   Global integrability, boundary value problem, anisotropic functional, obstacle problem.

Full text (PDF) (free access)

DOI: 10.3336/gm.51.1.13

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