# Layer potentials for general linear elliptic systems

@article{Barton2017LayerPF, title={Layer potentials for general linear elliptic systems}, author={Ariel Barton}, journal={arXiv: Analysis of PDEs}, year={2017} }

In this paper we construct layer potentials for elliptic differential operators using the Lax-Milgram theorem, without recourse to the fundamental solution; this allows layer potentials to be constructed in very general settings. We then generalize several well known properties of layer potentials for harmonic and second order equations, in particular the Green's formula, jump relations, adjoint relations, and Verchota's equivalence between well-posedness of boundary value problems and… Expand

#### 14 Citations

The Neumann problem for higher order elliptic equations

- Mathematics
- 2019

Abstract We solve the Neumann problem in the half space for higher order elliptic differential equations with variable self-adjoint t-independent coefficients, and with boundary data in the negative… Expand

THE L NEUMANN PROBLEM FOR HIGHER ORDER ELLIPTIC EQUATIONS

- 2020

We solve the Neumann problem in the half space R + , for higher order elliptic differential equations with variable self-adjoint t-independent coefficients, and with boundary data in Lp, where max (… Expand

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

- Mathematics
- 2018

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… Expand

Newtonian and Single Layer Potentials for the Stokes System with L∞ Coefficients and the Exterior Dirichlet Problem

- Mathematics
- Trends in Mathematics
- 2019

A mixed variational formulation of some problems in L2-based Sobolev spaces is used to define the Newtonian and layer potentials for the Stokes system with L∞ coefficients on Lipschitz domains in… Expand

The Neumann problem for higher order elliptic equations with symmetric coefficients

- Mathematics
- 2017

In this paper we establish well posedness of the Neumann problem with boundary data in $$L^2$$L2 or the Sobolev space $$\dot{W}^2_{-1}$$W˙-12, in the half space, for linear elliptic differential… Expand

THE Ẇ−1,p NEUMANN PROBLEM FOR HIGHER ORDER ELLIPTIC EQUATIONS

- 2019

We solve the Neumann problem in the half space R + , for higher order elliptic differential equations with variable self-adjoint t-independent coefficients, and with boundary data in the negative… Expand

Critical Perturbations for Second Order Elliptic Operators. Part I: Square function bounds for layer potentials

- Mathematics
- 2020

This is the first part of a series of two papers where we study perturbations of divergence form second order elliptic operators $-\mathop{\operatorname{div}} A \nabla$ by first and zero order terms,… Expand

Layer potential theory for the anisotropic Stokes system with variable
L
∞
symmetrically elliptic tensor coefficient

- Mathematics
- 2021

EPSRC grant EP/M013545/1: "Mathematical Analysis of Boundary-Domain Integral Equations for Nonlinear PDEs"; Babes-Bolyai University research grant AGC35124/31.10.2018; Deutsche Forschungsgemeinschaft… Expand

Potentials and transmission problems in weighted Sobolev spaces for anisotropic Stokes and Navier–Stokes systems with L∞ strongly elliptic coefficient tensor

- Mathematics, Physics
- Complex Variables and Elliptic Equations
- 2019

ABSTRACT We obtain well-posedness results in -based weighted Sobolev spaces for a transmission problem for anisotropic Stokes and Navier–Stokes systems with strongly elliptic coefficient tensor, in… Expand

Trace and extension theorems relating Besov spaces to weighted averaged Sobolev spaces

- Mathematics
- 2016

There are known trace and extension theorems relating functions in a weighted Sobolev space in a domain U to functions in a Besov space on the boundary bU. We extend these theorems to the case where… Expand

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