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.


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DOI: 10.3336/gm.51.1.13


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