Displaying similar documents to “Area integral estimates for higher order elliptic equations and systems”

The Dirichlet problem for elliptic equations with drift terms.

Carlos E. Kenig, Jill Pipher (2001)

Publicacions Matemàtiques

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We establish absolute continuity of the elliptic measure associated to certain second order elliptic equations in either divergence or nondivergence form, with drift terms, under minimal smoothness assumptions on the coefficients.

Hardy spaces and the Dirichlet problem on Lipschitz domains.

Carlos E. Kenig, Jill Pipher (1987)

Revista Matemática Iberoamericana

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Our concern in this paper is to describe a class of Hardy spaces H(D) for 1 ≤ p < 2 on a Lipschitz domain D ⊂ R when n ≥ 3, and a certain smooth counterpart of H(D) on R, by providing an atomic decomposition and a description of their duals.

Boundary value problems for elliptic equations.

Carlos E. Kenig (1991)

Publicacions Matemàtiques

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In this note I will describe some recent results, obtained jointly with R. Fefferman and J. Pipher [RF-K-P], on the Dirichlet problem for second-order, divergence form elliptic equations, and some work in progress with J. Pipher [K-P] on the corresponding results for the Neumann and regularity problems.

A note on the Rellich formula in Lipschitz domains.

Alano Ancona (1998)

Publicacions Matemàtiques

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Let L be a symmetric second order uniformly elliptic operator in divergence form acting in a bounded Lipschitz domain ­Ω of R and having Lipschitz coefficients in Ω­. It is shown that the Rellich formula with respect to Ω­ and L extends to all functions in the domain D = {u ∈ H (Ω­); L(u) ∈ L(­Ω)} of L. This answers a question of A. Chaïra and G. Lebeau.

The Dirichlet problem for the biharmonic equation in a Lipschitz domain

Björn E. J. Dahlberg, C. E. Kenig, G. C. Verchota (1986)

Annales de l'institut Fourier

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In this paper we study and give optimal estimates for the Dirichlet problem for the biharmonic operator Δ 2 , on an arbitrary bounded Lipschitz domain D in R n . We establish existence and uniqueness results when the boundary values have first derivatives in L 2 ( ∂ D ) , and the normal derivative is in L 2 ( ∂ D ) . The resulting solution u takes the boundary values in the sense of non-tangential convergence, and the non-tangential maximal function of ∇ u is shown to be in L 2 ( ∂ D ) .