Riesz transform on exterior Lipschitz domains and applications

Boundary value problems for second-order elliptic equations (35J25) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Harmonic analysis and PDEs (42B37)

Cites Work

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Gaussian heat kernel bounds through elliptic Moser iteration
$W^{1,p}$ estimates for elliptic problems with Neumann boundary conditions in Lipschitz domains
Elliptic equations in divergence form with partially BMO coefficients
Quasiconformal mappings and extendability of functions in Sobolev spaces
Boundary layers on Sobolev-Besov spaces and Poisson's equation for the Laplacian in Lipschitz domains
Dirichlet and Neumann exterior problems for the $n$-dimensional Laplace operator. An approach in weighted Sobolev spaces
Riesz transform, Gaussian bounds and the method of wave equation
Bounds of Riesz transforms on $L^p$ spaces for second order elliptic operators.
Uniform, Sobolev extension and quasiconformal circle domains
Plancherel-type estimates and sharp spectral multipliers
The global behavior of heat kernels in exterior domains
The inhomogeneous Dirichlet problem in Lipschitz domains
Riesz transform via heat kernel and harmonic functions on non-compact manifolds
Riesz transform under perturbations via heat kernel regularity
Gradient estimates for heat kernels and harmonic functions
Riesz transform and $L^p$-cohomology for manifolds with Euclidean ends
The L$^p$-integrability of the partial derivatives of a quasiconformal mapping
On the existence of certain singular integrals
Riesz transform on manifolds and heat kernel regularity
Elliptic equations with BMO coefficients in Reifenberg domains
Parabolic and Elliptic Equations with VMO Coefficients
Classical Fourier Analysis
Riesz transforms in one dimension
Injectivity theorems in plane and space
Riesz transforms for $1\le p\le 2$
The Inhomogeneous Neumann Problem in Lipschitz Domains
Riesz Transforms Outside a Convex Obstacle
The Conormal Derivative Problem for Elliptic Equations with BMO Coefficients on Reifenberg flat domains
Dirichlet heat kernel in the exterior of a compact set
Elliptic equations with BMO coefficients in Lipschitz domains
Sur les fonctions conjuguées.
Square roots of elliptic second order divergence operators on strongly Lipschitz domains: $L^p$ theory

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