Izvorni znanstveni članak

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

Sažetak

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.

Ključne riječi

Global integrability; boundary value problem; anisotropic functional; obstacle problem

Hrčak ID:

160114

URI

https://hrcak.srce.hr/160114

Datum izdavanja:

15.6.2016.

Posjeta: 649 *