Displaying similar documents to “Corrections to my paper “A Sturm-Liouville theorem for nonlinear elliptic partial differential equations””

Averaging for ordinary differential equations perturbed by a small parameter

Mustapha Lakrib, Tahar Kherraz, Amel Bourada (2016)

Mathematica Bohemica

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In this paper, we prove and discuss averaging results for ordinary differential equations perturbed by a small parameter. The conditions we assume on the right-hand sides of the equations under which our averaging results are stated are more general than those considered in the literature. Indeed, often it is assumed that the right-hand sides of the equations are uniformly bounded and a Lipschitz condition is imposed on them. Sometimes this last condition is relaxed to the uniform continuity...

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

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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.

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 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.