Displaying similar documents to “ L p -Estimates for linear elliptic systems with discontinuous coefficients”

H ∞ functional calculus for an elliptic operator on a half-space with general boundary conditions

Giovanni Dore, Alberto Venni (2002)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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Let A be the L p realization ( 1 < p < ∞ ) of a differential operator P ( D x , D t ) on ℝ n × ℝ + with general boundary conditions B k ( D x , D t ) u ( x , 0 ) = 0 ( 1 ≤ k ≤ m ). Here P is a homogeneous polynomial of order 2 m in n + 1 complex variables that satisfies a suitable ellipticity condition, and for 1 ≤ k ≤ m B k is a homogeneous polynomial of order m k < 2 m ; it is assumed that the usual complementing condition is satisfied. We prove that A is a sectorial operator with a bounded H ∞ functional calculus.

Hölder a priori estimates for second order tangential operators on CR manifolds

Annamaria Montanari (2003)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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On a real hypersurface M in ℂ n + 1 of class C 2 , α we consider a local CR structure by choosing n complex vector fields W j in the complex tangent space. Their real and imaginary parts span a 2 n -dimensional subspace of the real tangent space, which has dimension 2 n + 1 . If the Levi matrix of M is different from zero at every point, then we can generate the missing direction. Under this assumption we prove interior a priori estimates of Schauder type for solutions of a class of second order partial differential...