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1

Lower semicontinuity of variational integrals on elliptic complexes

100%

Verde A.

Studia Mathematica

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2011

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tom 204

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nr 3

283-294

EN

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

Variational integrals for elliptic complexes

63%

Giannetti F., Verde A.

Studia Mathematica

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2000

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tom 140

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nr 1

79-98

EN

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

Morrey regularity and continuity results for almost minimizers of asymptotically convex integrals

51%

Foss M., di Napoli A., Verde A.

Applicationes Mathematicae

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2008

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tom 35

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nr 3

335-353

EN

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.

Ograniczanie wyników

2 Studia Mathematica

1 Applicationes Mathematicae

3 Verde A.

1 Foss M.

1 Giannetti F.

1 di Napoli A.

1 2011

1 2008

1 2000

Lower semicontinuity of variational integrals on elliptic complexes

Variational integrals for elliptic complexes

Morrey regularity and continuity results for almost minimizers of asymptotically convex integrals