1,720,972 research outputs found
Rigidity for perimeter inequalities under symmetrization: State of the art and open problems
No full textWe review some classical results in symmetrization theory, some recent progress in understanding rigidity, and indicate some open problems
A Vanishing Viscosity Approach to Fracture Growth in a Cohesive Zone Model with Prescribed Crack Path
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<i>k</i>-quasi-convexity reduces to quasi-convexity
No full textThe relation between quasi-convexity and k-quasi-convexity, k ≥ 2, is investigated. It is shown that every smooth strictly k-quasi-convex integrand with p-growth at infinity, p > 1, is the restriction to kth-order symmetric tensors of a quasi-convex function with the same growth. When the smoothness condition is dropped, it is possible to prove an approximation result. As a consequence, lower semicontinuity results for kth-order variational problems are deduced as corollaries of well-known first-order theorems. This generalizes a previous work by Dal Maso et al., in which the case where k = 2 was treated.</jats:p
Optimal Regularity and Structure of the Free Boundary for Minimizers in Cohesive Zone Models
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An extension theorem in SBV and an application to the homogenization of the Mumford-Shah functional in perforated domains
Full text linkThe aim of this paper is to prove the existence of extension operators for SBV functions from periodically perforated domains. This result will be the fundamental tool to prove the compactness in a non coercive homogenization problem
Convergence of a semi-discretization scheme for the Hamilton-Jacobi equation: a new approach with the adjoint method
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