Glasnik matematički, Vol. 51 No. 1, 2016.
Original scientific paper
https://doi.org/10.3336/gm.51.1.13
Global integrability for solutions to boundary value problems of anisotropic functionals
Hongya Goa
; College of Mathematics and Information Science, Hebei University, 071002 Baoding, China
Shuang Liang
; College of Mathematics and Information Science, Hebei University, 071002 Baoding, China
Yi Cui
; College of Mathematics and Information Science, Hebei University, 071002 Baoding, China
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.
Keywords
Global integrability; boundary value problem; anisotropic functional; obstacle problem
Hrčak ID:
160114
URI
Publication date:
15.6.2016.
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