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A maximum principle for biharmonic functions in Lipschitz and C1 domains.

J. Pipher; G. Verchota — 1993

Commentarii mathematici Helvetici

Nonvariational layer potentials with respect to Hölder continuous vector fields.

G. C. Verchota — 2007

Revista Matemática Iberoamericana

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

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 $L^{2} (\partial D)$ , and the normal derivative is in $L^{2} (\partial D)$ . The resulting solution $u$ takes the boundary values in the sense of non-tangential convergence, and the non-tangential maximal function of $\nabla u$ is shown to be in $L^{2} (\partial D)$ .

Area integral estimates for higher order elliptic equations and systems

Björn E. J. Dahlberg; Carlos E. Kenig; Jill Pipher; G. C. Verchota — 1997

Annales de l'institut Fourier

Let $L$ be an elliptic system of higher order homogeneous partial differential operators. We establish in this article the equivalence in $L^{p}$ norm between the maximal function and the square function of solutions to $L$ in Lipschitz domains. Several applications of this result are discussed.

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Currently displaying 1 – 4 of 4

A maximum principle for biharmonic functions in Lipschitz and C1 domains.

Nonvariational layer potentials with respect to Hölder continuous vector fields.

The Dirichlet problem for the biharmonic equation in a Lipschitz domain

Area integral estimates for higher order elliptic equations and systems