We prove a lower semicontinuity result for variational integrals associated with a given first order elliptic complex, extending, in this general setting, a well known result in the case $𝓓'(ℝⁿ,ℝ) → \limits^{∇} 𝓓'(ℝⁿ,ℝⁿ) →\limits^{curl} 𝓓'(ℝⁿ,ℝ^{n×n})$.
2
Dostęp do pełnego tekstu na zewnętrznej witrynie WWW
We discuss variational integrals which are defined on differential forms associated with a given first order elliptic complex. This general framework provides us with better understanding of the concepts of convexity, even in the classical setting $D'(ℝ^n,ℝ) {∇\over →} D'(ℝ^n,ℝ^n) {{curl}\over{→}} D'(ℝ^n,ℝ^{n×n})$
3
Dostęp do pełnego tekstu na zewnętrznej witrynie WWW
In a recent paper [Forum Math., 2008] the authors established some global, up to the boundary of a domain Ω ⊂ ℝⁿ, continuity and Morrey regularity results for almost minimizers of functionals of the form $u ↦ ∫_{Ω} g(x,u(x),∇u(x)) dx$. The main assumptions for these results are that g is asymptotically convex and that it satisfies some growth conditions. In this article, we present a specialized but significant version of this general result. The primary purpose of this paper is provide several applications of this simplified result.
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.