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On morrey spaces in the calculus of variations
We prove some global Morrey regularity results for almost minimizers of functionals of the form uW fx,u,1u dx. This regularity is valid up to the boundary, provided the boundary data are sufficiently regular. The main assumption on f is that for each x and u, the function f(x, u, ·) behaves asymptotically like the function h(:·:)α( x), where h is an N-function. ^ Following this, we provide a characterization of the class of Young measures that can be generated by a sequence of functions &cubl0;fj&cubr0;∞ j=1 uniformly bounded in the Morrey space Lp ,λ(Ω; RN ) with &cubl0;&vbm0;fj&vbm0;p &cubr0;∞j=1 equiintegrable. We then treat the case that each f j = ∇uj for some uj ∈ W 1,p(Ω; RN ).^ Lastly, we provide applications of and connections between these results. ^
Fey, Kyle, "On morrey spaces in the calculus of variations" (2011). ETD collection for University of Nebraska - Lincoln. AAI3449403.