Descriptor: "Blow-up limit" / Publication Year Range: Last 10 years - Searchworks@Jio Institute Digital Library Search Results

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Author: Fang, Yangqin
Subjects: *HAUSDORFF measures, *SOAP
Abstract: In this paper, we will give a C1,β-regularity result on the boundary for two dimensional sliding almost minimal sets in R3. This effect may apply to the regularity of the soap films at the boundary, and may also lead to the existence of a solution to the Plateau problem with sliding boundary conditions proposed by Guy David in the case that the boundary is a 2-dimensional smooth submanifold. [ABSTRACT FROM AUTHOR]
Published: 2021
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Author: Fang, Yangqin
Subjects: HAUSDORFF measures, SOAP
Abstract: In this paper, we will give a C1,β-regularity result on the boundary for two dimensional sliding almost minimal sets in R3. This effect may apply to the regularity of the soap films at the boundary, and may also lead to the existence of a solution to the Plateau problem with sliding boundary conditions proposed by Guy David in the case that the boundary is a 2-dimensional smooth submanifold. [ABSTRACT FROM AUTHOR]
Published: 2021
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Author: Veronica Felli, Enrico Valdinoci, Serena Dipierro, Dipierro, S, Felli, V, and Valdinoci, E
Subjects: Blow-up limit, Singular weight, Mathematics::Analysis of PDEs, Conical geometry, Boundary (topology), 01 natural sciences, 010305 fluids & plasmas, Mathematics - Analysis of PDEs, Operator (computer programming), 0103 physical sciences, FOS: Mathematics, Neumann boundary condition, 0101 mathematics, MAT/05 - ANALISI MATEMATICA, Unique continuation, Mathematical Physics, Mathematics, Forcing (recursion theory), Applied Mathematics, 010102 general mathematics, Mathematical analysis, Almgren's frequency formula, Cone (category theory), Elliptic curve, Vertex (curve), Gravitational singularity, Analysis, Analysis of PDEs (math.AP)
Abstract: We consider an elliptic equation in a cone, endowed with (possibly inhomogeneous) Neumann conditions. The operator and the forcing terms can also allow non-Lipschitz singularities at the vertex of the cone. In this setting, we provide unique continuation results, both in terms of interior and boundary points. The proof relies on a suitable Almgren-type frequency formula with remainders. As a byproduct, we obtain classification results for blow-up limits.
Published: 2020
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Author: Lemenant, Antoine
Subjects: *GEOMETRIC rigidity, *DIMENSION theory (Algebra), *BLOWING up (Algebraic geometry), *MATHEMATICAL proofs, *MONOTONIC functions
Abstract: We study global Mumford–Shah minimizers in R N , introduced by Bonnet as blow-up limits of Mumford–Shah minimizers. We prove a new monotonicity formula for the energy of u when the singular set K is contained in an ( N − 1 ) -dimensional cone. We then use this monotonicity to prove that for any reduced global minimizer ( u , K ) in R 3 , if K is contained in a half-plane and touches its edge, then it is the half-plane itself. This partially answers to a question of Guy David. [ABSTRACT FROM AUTHOR]
Published: 2015
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Author: Dipierro, S, Felli, V, Valdinoci, E, Dipierro S., Felli V., Valdinoci E., Dipierro, S, Felli, V, Valdinoci, E, Dipierro S., Felli V., and Valdinoci E.
Abstract: We consider an elliptic equation in a cone, endowed with (possibly inhomogeneous) Neumann conditions. The operator and the forcing terms can also allow non-Lipschitz singularities at the vertex of the cone. In this setting, we provide unique continuation results, both in terms of interior and boundary points. The proof relies on a suitable Almgren-type frequency formula with remainders. As a byproduct, we obtain classification results for blow-up limits.
Published: 2020

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