Criterion for the Sobolev well-posedness of the Dirichlet problem for the Poisson equation in Lipschitz domains. I
From MaRDI portal
Publication:2227034
DOI10.33048/semi.2020.17.144zbMath1459.35102OpenAlexW3197324005MaRDI QIDQ2227034
Publication date: 9 February 2021
Published in: Sibirskie Èlektronnye Matematicheskie Izvestiya (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.33048/semi.2020.17.144
Boundary value problems for second-order elliptic equations (35J25) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05)
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
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- On the existence of boundary values for harmonic functions in several variables
- A weighted a priori estimate in rectifiable domains of local Lyapunov-Dini type
- Error bound for a generalized M. A. Lavrentiev's formula via the norm in a fractional Sobolev space
- Boundary value problems for the Laplacian in convex and semiconvex domains
- Maximal \(L^{p}\)-regularity for the Laplacian on Lipschitz domains
- A \(W^{1,p}\)-estimate for solutions to mixed boundary value problems for second order elliptic differential equations
- A generalisation of Widman's theorem on comparison domains for harmonic measures
- The Green function for uniformly elliptic equations
- Eigenvalue inequalities for the Dirichlet problem on spheres and the growth of subharmonic functions
- Comparisons of Kernel functions, boundary Harnack principle and relative Fatou theorem on Lipschitz domains
- Principle de Harnack à la frontière et théorème de Fatou pour un opérateur elliptique dans un domaine lipschitzien
- Estimates of harmonic measure
- Index of the closure of the operator of the Dirichlet problem in a domain with an irregular boundary
- Boundary layers on Sobolev-Besov spaces and Poisson's equation for the Laplacian in Lipschitz domains
- Positivity for a strongly coupled elliptic system by Green function estimates
- Cauchy problem for the Kuznetsov equation
- Fundamental matrices and Green matrices for non-homogeneous elliptic systems
- Bounds of Riesz transforms on \(L^p\) spaces for second order elliptic operators.
- Integrability of Green potentials in fractal domains
- Zur Symmetrisierung von Funktionen auf Sphären
- Gradient estimates for harmonic and \(q\)-harmonic functions of symmetric stable processes.
- The inhomogeneous Dirichlet problem in Lipschitz domains
- Estimates for Green's matrices of elliptic systems by \(L^ p\) theory
- Sharp estimates for the Green function in Lipschitz domains
- Extremal barriers on cones with Phragmén-Lindelöf theorems and other applications
- On Dirichlet's boundary value problem. An \(L^p\)-theory based on a generalization of Garding's inequality
- The L\(^p\)-integrability of the partial derivatives of a quasiconformal mapping
- Über Wachstumseigenschaften gewisser Klassen von subharmonischen Funktionen
- On the Regularity of Green Functions in Lipschitz Domains
- Potential Space Estimates for Green Potentials in Convex Domains
- Elliptic equations with BMO coefficients in Reifenberg domains
- $L^q$-estimates for Green potentials in Lipschitz domains.
- Estimates in 𝐿_{𝑝} and in Hölder classes and the Miranda-Agmon maximum principle for solutions of elliptic boundary value problems in domains with singular points on the boundary
- Weighted spaces with nonhomogeneous norms and boundary value problems in domains with conical points
- Theory of Sobolev Multipliers
- Equivalence between the boundary Harnack principle and the Carleson estimate
- Multiple Integrals in the Calculus of Variations and Nonlinear Elliptic Systems. (AM-105)
- On Strong Barriers and an Inequality of Hardy for Domains in R n
- Elliptic boundary value problems in unbounded domains with noncompact and nonsmooth boundaries
- $ L_p$-estimates of the solution of the Dirichlet problem for second-order elliptic equations
- Various domain constants related to uniform perfectness
- An identity with applications to harmonic measure
- 17.—An Upper Bound for the Largest Zero of Hermite's Function with Applications to Subharmonic Functions
- Inequalities and monotonicity properties for zeros of Hermite functions
- Nonlinear equations and weighted norm inequalities
- Integrability of Superharmonic Functions and Subharmonic Functions
- HÖLDER CONTINUITY OF THE DIRICHLET SOLUTION FOR A GENERAL DOMAIN
- Dicrete Hölder estimates for a certain kind of parametrix. II
- Sobolev Spaces, Their Generalizations and Elliptic Problems in Smooth and Lipschitz Domains
- Positive Harmonic Functions on Lipschitz Domains
- Estimates of harmonic measures
- Boundary Harnack principle and Martin boundary for a uniform domain