The Ẇ−1,p Neumann problem for higher order elliptic equations

DOI10.1080/03605302.2020.1871364zbMath1481.35161arXiv1906.12234OpenAlexW3129352199MaRDI QIDQ5164828

Publication date: 15 November 2021

Published in: Communications in Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1906.12234

zbMATH Keywords

Neumann problem higher-order elliptic equation layer potentials

Mathematics Subject Classification ID

Boundary value problems for higher-order elliptic equations (35J40) Integral representations of solutions to PDEs (35C15)

Cites Work

Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
The Dirichlet problem for elliptic systems with data in Köthe function spaces
Boundary value problems and integral operators for the bi-Laplacian in non-smooth domains
The Dirichlet problem for higher order equations in composition form
Multi-layer potentials and boundary problems for higher-order elliptic systems in Lipschitz domains
Layer potentials and boundary value problems for elliptic equations with complex $L^\infty$ coefficients satisfying the small Carleson measure norm condition
On domain of Poisson operators and factorization for divergence form elliptic operators
Optimal estimates for the inhomogeneous problem for the bi-Laplacian in three-dimensional Lipschitz domains
A bilinear estimate for biharmonic functions in Lipschitz domains
Analyticity of layer potentials and $L^{2}$ solvability of boundary value problems for divergence form elliptic equations with complex $L^{\infty }$ coefficients
Solvability of elliptic systems with square integrable boundary data
Gradient estimates and the fundamental solution for higher-order elliptic systems with rough coefficients
Layer potentials and boundary value problems for elliptic systems in Lipschitz domains
The $L^p$ Dirichlet problem for elliptic systems on Lipschitz domains
Boundary value problems for the systems of elastostatics in Lipschitz domains
Functional calculus of Dirac operators and complex perturbations of Neumann and Dirichlet problems
The Dirichlet problem in Lipschitz domains for higher order elliptic systems with rough coefficients
Layer potentials and regularity for the Dirichlet problem for Laplace's equation in Lipschitz domains
The Dirichlet problem for the biharmonic equation in a Lipschitz domain
Adjoint boundary value problems for the biharmonic equation on $C^ 1$ domains in the plane
Hardy spaces and the Neumann problem in $L^ p$ for Laplace's equation in Lipschitz domains
The Dirichlet problem in non-smooth domains
Potential techniques for boundary value problems on $C^1$-domains
Boundary layers on Sobolev-Besov spaces and Poisson's equation for the Laplacian in Lipschitz domains
The Neumann problem for elliptic equations with non-smooth coefficients
A new approach to absolute continuity of elliptic measure, with applications to non-symmetric equations
Equivalence between regularity theorems and heat kernel estimates for higher-order elliptic operators and systems under divergence form
Representation and uniqueness for boundary value elliptic problems via first order systems
The Neumann problem for higher order elliptic equations with symmetric coefficients
The Dirichlet problem for the Stokes system on Lipschitz domains
Sharp estimates for Green potentials on non-smooth domains
The inhomogeneous Dirichlet problem in Lipschitz domains
Functional calculus for a class of complex elliptic operators in dimension one (and applications to some complex elliptic equations in dimension two).
Dilation invariant estimates and the boundary Gårding inequality for higher order elliptic operators
Maximum principles for the polyharmonic equation on Lipschitz domains
Dirichlet and Neumann boundary values of solutions to higher order elliptic equations
The regularity problem for second order elliptic operators with complex-valued bounded measurable coefficients
Necessary and sufficient conditions for the solvability of the $L^p$ Dirichlet problem on Lipschitz domains
The $L^{p}$ boundary value problems on Lipschitz domains
The biharmonic Neumann problem in Lipschitz domains
Layer potentials beyond singular integral operators
On Poisson operators and Dirichlet-Neumann maps in $H^s$ for divergence form elliptic operators with Lipschitz coefficients
Functional calculus for first order systems of Dirac type and boundary value problems
Boundary layers, Rellich estimates and extrapolation of solvability for elliptic systems
The method of layer potentials inL^pand endpoint spaces for elliptic operators withL^∞coefficients
On the Regularity of Green Functions in Lipschitz Domains
Multiple layer potentials and the dirichlet problem for higher order elliptic equations in the plane I
The regularity and Neumann problem for non-symmetric elliptic operators
A survey on boundary conditions for the biharmonic
Multiple Integrals in the Calculus of Variations and Nonlinear Elliptic Systems. (AM-105)
On the Poisson integral for Lipschitz and $C^{1}$-domains
The Neumann problem on Lipschitz domains
The Dirichlet Problem in L p for the Biharmonic Equation on Lipschitz Domains
Some observations on Besov and Lizorkin-Triebel spaces.
The Inhomogeneous Neumann Problem in Lipschitz Domains
Higher-Order Elliptic Equations in Non-Smooth Domains: a Partial Survey
Square function estimates on layer potentials for higher‐order elliptic equations
Layer potentials for general linear elliptic systems
Elliptic Boundary Value Problems with Fractional Regularity Data
A new system of boundary integral equations for plates with free edges
Elliptic Partial Differential Equations with Almost-Real Coefficients
Boundary Coerciveness and the Neumann Problem for 4th Order Linear Partial Differential Operators
Non-unique solutions to boundary value problems for non-symmetric divergence form equations
Layer Potentials and Boundary-Value Problems for Second Order Elliptic Operators with Data in Besov Spaces
Square function/non-tangential maximal function estimates and the Dirichlet problem for non-symmetric elliptic operators

This page was built for publication: The Ẇ−1,p Neumann problem for higher order elliptic equations