Displaying similar documents to “Only one of generalized gradients can be elliptic”

Refined Kato inequalities in riemannian geometry

Marc Herzlich (2000)

Journées équations aux dérivées partielles

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We describe the recent joint work of the author with David M. J. Calderbank and Paul Gauduchon on refined Kato inequalities for sections of vector bundles living in the kernel of natural first-order elliptic operators.

Extended Maximum Principles

Al-Mahameed, M. M. (2007)

Serdica Mathematical Journal

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2000 Mathematics Subject Classification: 35B50, 35L15. In this paper we introduce some new results concerning the maximum principles for second order linear elliptic partial differential equations defined on a noncompact Riemannian manifold.

A characterization of elliptic operators

Grzegorz Łysik, Paweł M. Wójcicki (2014)

Annales Polonici Mathematici

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We give a characterization of constant coefficients elliptic operators in terms of estimates of their iterations on smooth functions.

On a class of nonlocal elliptic operators for compact Lie groups. Uniformization and finiteness theorem

Boris Sternin (2011)

Open Mathematics

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We consider a class of nonlocal operators associated with an action of a compact Lie group G on a smooth closed manifold. Ellipticity condition and Fredholm property for elliptic operators are obtained. This class of operators is studied using pseudodifferential uniformization, which reduces the problem to a pseudodifferential operator acting in sections of infinite-dimensional bundles.

On Dittmar's approach to the Beltrami equation

Ewa Ligocka (2002)

Colloquium Mathematicae

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We recall an old result of B. Dittmar. This result permits us to obtain an existence theorem for the Beltrami equation and some other results as a direct consequence of Moser's classical estimates for elliptic operators.

Continuity of solutions of linear, degenerate elliptic equations

Jani Onninen, Xiao Zhong (2007)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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We consider the simplest form of a second order, linear, degenerate, elliptic equation with divergence structure in the plane. Under an integrability condition on the degenerate function, we prove that the solutions are continuous.

Nonlinear elliptic equations involving critical Sobolev exponent on compact Riemannian manifolds in presence of symmetries.

Zindine Djadli (1999)

Revista Matemática Complutense

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In this paper, we study a nonlinear elliptic equation with critical exponent, invariant under the action of a subgroup G of the isometry group of a compact Riemannian manifold. We obtain some existence results of positive solutions of this equation, and under some assumptions on G, we show that we can solve this equation for supercritical exponents.