scholarly journals Boundedness of single layer potentials associated to divergence form parabolic equations with complex coefficients

2016 ◽  
Vol 55 (5) ◽  
Author(s):  
Alejandro J. Castro ◽  
Kaj Nyström ◽  
Olow Sande
Keyword(s):  
Parabolic Equations ◽  
Single Layer ◽  
Divergence Form ◽  
Layer Potentials ◽  
Complex Coefficients

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 Nontangential Estimates on Layer Potentials and the Neumann Problem for Higher-Order Elliptic Equations

2020 ◽  
Author(s):  
Ariel Barton ◽  
Steve Hofmann ◽  
Svitlana Mayboroda
Keyword(s):  
Neumann Problem ◽  
Elliptic Equations ◽  
Divergence Form ◽  
Higher Order ◽  
Elliptic Operators ◽  
Layer Potentials ◽  
The Neumann Problem

Abstract We solve the Neumann problem, with nontangential estimates, for higher-order divergence form elliptic operators with variable $t$-independent coefficients. Our results are accompanied by nontangential estimates on higher-order layer potentials.

Perturbation and Solvability of Initial Lp Dirichlet Problems for Parabolic Equations over Non-cylindrical Domains

2014 ◽  
Vol 66 (2) ◽  
pp. 429-452 ◽  
Author(s):  
Jorge Rivera-Noriega
Keyword(s):  
Dirichlet Problem ◽  
Parabolic Equations ◽  
Elliptic Equations ◽  
Carleson Measure ◽  
Divergence Form ◽  
Second Order ◽  
Linear Operators ◽  
Dirichlet Problems ◽  
Small Perturbations ◽  
Cylindrical Domains

AbstractFor parabolic linear operators L of second order in divergence form, we prove that the solvability of initial Lp Dirichlet problems for the whole range 1 < p < ∞ is preserved under appropriate small perturbations of the coefficients of the operators involved. We also prove that if the coefficients of L satisfy a suitable controlled oscillation in the form of Carleson measure conditions, then for certain values of p > 1, the initial Lp Dirichlet problem associated with Lu = 0 over non-cylindrical domains is solvable. The results are adequate adaptations of the corresponding results for elliptic equations.

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