scholarly journals L2-boundedness of gradients of single-layer potentials and uniform rectifiability

2021 ◽  
Vol 14 (3) ◽  
pp. 717-791
Author(s):  
Laura Prat ◽  
Carmelo Puliatti ◽  
Xavier Tolsa
Keyword(s):  
Single Layer ◽  
Layer Potentials ◽  
Uniform Rectifiability

On norm of single layer potentials on segments

2016 ◽  
Vol 22 (1) ◽  
Author(s):  
Seyed M. Zoalroshd
Keyword(s):  
Upper Bound ◽  
Single Layer ◽  
Exact Expression ◽  
Operator Norm ◽  
Equal Length ◽  
Layer Potentials ◽  
Schmidt Norm ◽  
Special Case

AbstractWe show that, for a special case, equality of the spectra of single layer potentials defined on two segments implies that these segments must have equal length. We also provide an upper bound for the operator norm and exact expression for the Hilbert–Schmidt norm of single layer potentials on segments.

scholarly journals Single layer potentials on surfaces with small Lipschitz constants

2014 ◽  
Vol 418 (2) ◽  
pp. 676-712 ◽  
Author(s):  
Vladimir Kozlov ◽  
Johan Thim ◽  
Bengt Ove Turesson
Keyword(s):  
Single Layer ◽  
Layer Potentials ◽  
Lipschitz Constants

Simply and doubly periodic arrangements of the equi-stress holes in a perforated elastic plane: The single-layer potential approach

2017 ◽  
Vol 23 (5) ◽  
pp. 805-819 ◽  
Author(s):  
Shmuel Vigdergauz
Keyword(s):  
Periodic Structures ◽  
Rotational Symmetry ◽  
Infinite Plate ◽  
Single Layer ◽  
Mapping Technique ◽  
Elastic Plane ◽  
Layer Potentials ◽  
Layer Potential ◽  
Linear Elastostatics ◽  
Wide Range

The layer potentials of two-dimensional linear elastostatics are applied as a novel building block for the semi-analytical design of non-standard arrangements of the equi-stress holes in an infinite plate under a given bulk-type loading. Thematically, this paper begins where our previous work left off with the main attention being focused on periodic structures of low rotational symmetry which are hard to tackle by the more customary conformal mapping technique. The analytical derivations are backed up by numerical simulations, in which a genetic algorithm is utilized to identify the optimal interface shapes for different geometries and a wide range of the governing parameters.

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