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On Morrey Spaces In The Calculus Of Variations, Kyle Fey
On Morrey Spaces In The Calculus Of Variations, Kyle Fey
Department of Mathematics: Dissertations, Theses, and Student Research
We prove some global Morrey regularity results for almost minimizers of functionals of the form u → ∫Ω f(x, u, ∇u)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 …