The \(L^ p\) Dirichlet problem for small perturbations of the Laplacian

DOI10.1007/BF02762711zbMath0853.35047MaRDI QIDQ1916901

Luis Escauriaza

Publication date: 5 January 1997

Published in: Israel Journal of Mathematics (Search for Journal in Brave)

zbMATH Keywords

harmonic measureDahlberg's conditionfunction of vanishing mean oscillation

Mathematics Subject Classification ID

Spaces of measurable functions ((L^p)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) (46E30) Second-order elliptic equations (35J15) Boundary values of solutions to elliptic equations and elliptic systems (35J67) Connections of harmonic functions with differential equations in higher dimensions (31B35)

Related Items (10)

Generalized Carleson perturbations of elliptic operators and applications ⋮ Divergence form operators in Reifenberg flat domains ⋮ Harmonic analysis on chord arc domains ⋮ Perturbation of elliptic operators in 1-sided NTA domains satisfying the capacity density condition ⋮ Optimal Poisson kernel regularity for elliptic operators with Hölder continuous coefficients in vanishing chord-arc domains ⋮ Elliptic measures for Dahlberg-Kenig-Pipher operators: asymptotically optimal estimates ⋮ Boundary rectifiability and elliptic operators with \(W^{1, 1}\) coefficients ⋮ Carleson perturbations of elliptic operators on domains with low dimensional boundaries ⋮ Perturbations of elliptic operators in 1-sided chord-arc domains. Part I: Small and large perturbation for symmetric operators ⋮ Perturbation theory for solutions to second order elliptic operators with complex coefficients and the \(L^p\) Dirichlet problem

Cites Work

• Unnamed Item
• Area integral estimates for elliptic differential operators with non- smooth coefficients
• The Dirichlet problem in non-smooth domains
• The Green function for uniformly elliptic equations
• The theory of weights and the Dirichlet problem for elliptic equations
• Large perturbations of elliptic operators and the solvability of the \(L^ p\) Dirichlet problem
• Weak type-\((1,1)\) inequalities and regularity properties of adjoint and normalized adjoint solutions to linear nondivergence form operators with VMO coefficients
• A Criterion for the Absolute Continuity of the Harmonic Measure Associated With an Elliptic Operator
• On the Absolute Continuity of Elliptic Measures
• On Harnack's theorem for elliptic differential equations
• Functions of Vanishing Mean Oscillation

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