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On morrey spaces in the calculus of variations
Abstract
We prove some global Morrey regularity results for almost minimizers of functionals of the form [special characters omitted] 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 [special characters omitted] uniformly bounded in the Morrey space Lp ,λ(Ω; [special characters omitted]) with [special characters omitted] equiintegrable. We then treat the case that each f j = ∇uj for some uj ∈ W 1,p(Ω; [special characters omitted]). Lastly, we provide applications of and connections between these results.
Subject Area
Applied Mathematics|Mathematics
Recommended Citation
Fey, Kyle, "On morrey spaces in the calculus of variations" (2011). ETD collection for University of Nebraska-Lincoln. AAI3449403.
https://digitalcommons.unl.edu/dissertations/AAI3449403