Book ChapterDOI
The Topological Degree
Vasile I. Istrăţescu
- pp 344-418
About:
The article was published on 1981-01-01. It has received 4 citations till now. The article focuses on the topics: Topological entropy in physics & Symmetry protected topological order.read more
Citations
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Journal ArticleDOI
Estimates for the topological degree and related topics
Abstract: This is a survey paper on estimates for the topological degree and related topics which range from the characterizations of Sobolev spaces and BV functions to the Jacobian determinant and nonlocal filter problems in Image Processing. These results are obtained jointly with Bourgain and Brezis. Several open questions are mentioned.
Journal ArticleDOI
Weak notions of Jacobian determinant and relaxation
TL;DR: In this paper, the distributional Jacobian and the relaxed total variation for Sobolev maps were studied and a weak notion of Jacobian determinant was proposed for the relaxation of polyconvex functionals.
Journal ArticleDOI
Weak lower semicontinuity for polyconvex integrals in the limit case
TL;DR: In this paper, a lower semicontinuity result for polyconvex functionals of the Calculus of Variations along sequences of maps was proved for polygonal functionals.
Journal ArticleDOI
Lower semi-continuity for non-coercive polyconvex integrals in the limit case*
TL;DR: Lower semi-continuity results for polyconvex functionals of the calculus of variations along sequences of maps u: Ω ⊂ n → ℝm in W1,m, 2 ⩽ m⩽ n, weakly converging in W 1,m-1, was established in this paper.
References
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Journal ArticleDOI
Estimates for the topological degree and related topics
Abstract: This is a survey paper on estimates for the topological degree and related topics which range from the characterizations of Sobolev spaces and BV functions to the Jacobian determinant and nonlocal filter problems in Image Processing. These results are obtained jointly with Bourgain and Brezis. Several open questions are mentioned.
Journal ArticleDOI
Weak notions of Jacobian determinant and relaxation
TL;DR: In this paper, the distributional Jacobian and the relaxed total variation for Sobolev maps were studied and a weak notion of Jacobian determinant was proposed for the relaxation of polyconvex functionals.
Journal ArticleDOI
Weak lower semicontinuity for polyconvex integrals in the limit case
TL;DR: In this paper, a lower semicontinuity result for polyconvex functionals of the Calculus of Variations along sequences of maps was proved for polygonal functionals.
Journal ArticleDOI
Lower semi-continuity for non-coercive polyconvex integrals in the limit case*
TL;DR: Lower semi-continuity results for polyconvex functionals of the calculus of variations along sequences of maps u: Ω ⊂ n → ℝm in W1,m, 2 ⩽ m⩽ n, weakly converging in W 1,m-1, was established in this paper.