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Mathematical analysis for the peridynamic nonlocal continuum theory*

Qiang Du, Kun Zhou (2011)

ESAIM: Mathematical Modelling and Numerical Analysis

We develop a functional analytical framework for a linear peridynamic model of a spring network system in any space dimension. Various properties of the peridynamic operators are examined for general micromodulus functions. These properties are utilized to establish the well-posedness of both the stationary peridynamic model and the Cauchy problem of the time dependent peridynamic model. The connections to the classical elastic models are also provided.

Maximal regularity for a class of integro-differential equations with infinite delay in Banach spaces

Valentin Keyantuo, Carlos Lizama (2005)

Studia Mathematica

We use Fourier multiplier theorems to establish maximal regularity results for a class of integro-differential equations with infinite delay in Banach spaces. Concrete equations of this type arise in viscoelasticity theory. Results are obtained for periodic solutions in the vector-valued Lebesgue and Besov spaces. An application to semilinear equations is considered.

On the structure of fixed point sets of some compact maps in the Fréchet space

Zbyněk Kubáček (1993)

Mathematica Bohemica

The aim of this note is 1. to show that some results (concerning the structure of the solution set of equations (18) and (21)) obtained by Czarnowski and Pruszko in [6] can be proved in a rather different way making use of a simle generalization of a theorem proved by Vidossich in [8]; and 2. to use a slight modification of the “main theorem” of Aronszajn from [1] applying methods analogous to the above mentioned idea of Vidossich to prove the fact that the solution set of the equation (24), (25)...

Sobolev and isoperimetric inequalities for Dirichlet forms on homogeneous spaces

Marco Biroli, Umberto Mosco (1995)

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

We prove local embeddings of Sobolev and Morrey type for Dirichlet forms on spaces of homogeneous type. Our results apply to some general classes of selfadjoint subelliptic operators as well as to Dirichlet operators on certain self-similar fractals, like the Sierpinski gasket. We also define intrinsic BV spaces and perimeters and prove related isoperimetric inequalities.

Solution operators for convolution equations on the germs of analytic functions on compact convex sets in ℂ N

S. Melikhov, Siegfried Momm (1995)

Studia Mathematica

G ⊂ ℂ N is compact and convex it is known for a long time that the nonzero constant coefficients linear partial differential operators (of finite or infinite order) are surjective on the space of all analytic functions on G. We consider the question whether solutions of the inhomogeneous equation can be given in terms of a continuous linear operator. For instance we characterize those sets G for which this is always the case.

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