کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4611649 | 1338634 | 2012 | 49 صفحه PDF | دانلود رایگان |

In this paper we are concerned with the regularity of minimizers u∈W1,p(Ω,RN)u∈W1,p(Ω,RN) of quasi-convex integral functionals of the typeF[u]:=∫Ωf(x,u,Du)dx. The crucial point here is that the integrand f admits very weak regularity properties. With respect to the gradient variable it satisfies degenerate/singular p-growth conditions without necessarily possessing a quasi-diagonal Uhlenbeck-type structure, and with respect to the x-variable the integrand might be even discontinuous. It is only assumed that a certain VMO-condition holds. Under those assumptions we prove partial Hölder continuity of minimizers, i.e. Hölder continuity of u for any Hölder exponent α∈(0,1)α∈(0,1) outside a set of measure zero. Under such weak assumptions regularity results for the gradient of minimizers is not expected to hold since even in the scalar case counterexamples to C1C1-regularity are known.
Journal: Journal of Differential Equations - Volume 252, Issue 2, 15 January 2012, Pages 1052–1100