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Eigenvalues of polyharmonic operators on variable domains

Davide Buoso, Pier Domenico Lamberti (2013)

ESAIM: Control, Optimisation and Calculus of Variations

We consider a class of eigenvalue problems for polyharmonic operators, including Dirichlet and buckling-type eigenvalue problems. We prove an analyticity result for the dependence of the symmetric functions of the eigenvalues upon domain perturbations and compute Hadamard-type formulas for the Frechét differentials. We also consider isovolumetric domain perturbations and characterize the corresponding critical domains for the symmetric functions of the eigenvalues. Finally, we prove that balls are...

Elliptic boundary value problem in Vanishing Mean Oscillation hypothesis

Maria Alessandra Ragusa (1999)

Commentationes Mathematicae Universitatis Carolinae

In this note the well-posedness of the Dirichlet problem (1.2) below is proved in the class H 0 1 , p ( Ω ) for all 1 < p < ∞ and, as a consequence, the Hölder regularity of the solution u . ℒ is an elliptic second order operator with discontinuous coefficients ( V M O ) and the lower order terms belong to suitable Lebesgue spaces.

Elliptic problems with integral diffusion

Yannick Sire (2011/2012)

Séminaire Laurent Schwartz — EDP et applications

In this paper, we review several recent results dealing with elliptic equations with non local diffusion. More precisely, we investigate several problems involving the fractional laplacian. Finally, we present a conformally covariant operator and the associated singular and regular Yamabe problem.

Elliptic Systems of Pseudodifferential Equations in the Refined Scale on a Closed Manifold

Vladimir A. Mikhailets, Aleksandr A. Murach (2008)

Bulletin of the Polish Academy of Sciences. Mathematics

We study a system of pseudodifferential equations which is elliptic in the Petrovskii sense on a closed smooth manifold. We prove that the operator generated by the system is a Fredholm operator in a refined two-sided scale of Hilbert function spaces. Elements of this scale are special isotropic spaces of Hörmander-Volevich-Paneah.

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