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Carleman estimates with two large parameters for second order operators and applications to elasticity with residual stress

Victor Isakov, Nanhee Kim (2008)

Applicationes Mathematicae

We derive Carleman type estimates with two large parameters for a general partial differential operator of second order. The weight function is assumed to be pseudo-convex with respect to the operator. We give applications to uniqueness and stability of the continuation of solutions and identification of coefficients for the Lamé system of dynamical elasticity with residual stress. This system is anisotropic and cannot be principally diagonalized, but it can be transformed into an "upper triangular"...

Characterization of some interpolation spaces (II)

Alessandra Lunardi (1982)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

Si caratterizzano alcuni spazi di interpolazione tra spazi di funzioni continue e domini di operatori ellittici del 2° ordine.

Characterization of the domain of an elliptic operator of infinitely many variables in L 2 μ spaces

Giuseppe Da Prato (1997)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

We consider an elliptic operator associated to a Dirichlet form corresponding to a differential stochastic equation of potential form. We characterize the domain of the operator as a subspace of W 2 , 2 μ , where m u is the invariant measure of the differential stochastic equation.

Characterization of the linear partial differential operators with constant coefficients that admit a continuous linear right inverse

B. A. Taylor, R. Meise, Dietmar Vogt (1990)

Annales de l'institut Fourier

Solving a problem of L. Schwartz, those constant coefficient partial differential operators P ( D ) are characterized that admit a continuous linear right inverse on ( Ω ) or 𝒟 ' ( Ω ) , Ω an open set in R n . For bounded Ω with C 1 -boundary these properties are equivalent to P ( D ) being very hyperbolic. For Ω = R n they are equivalent to a Phragmen-Lindelöf condition holding on the zero variety of the polynomial P .

Clifford-Hermite-monogenic operators

Freddy Brackx, Nele de Schepper, Frank Sommen (2006)

Czechoslovak Mathematical Journal

In this paper we consider operators acting on a subspace of the space L 2 ( m ; m ) of square integrable functions and, in particular, Clifford differential operators with polynomial coefficients. The subspace is defined as the orthogonal sum of spaces s , k of specific Clifford basis functions of L 2 ( m ; m ) . Every Clifford endomorphism of can be decomposed into the so-called Clifford-Hermite-monogenic operators. These Clifford-Hermite-monogenic operators are characterized in terms of commutation relations and they...

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