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Displaying similar documents to “Some results on elliptic and parabolic equations in Hilbert spaces”

New optimal regularity results for infinite-dimensional elliptic equations

Enrico Priola, Lorenzo Zambotti (2000)

Bollettino dell'Unione Matematica Italiana

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In questo articolo si ottengono stime di Schauder di tipo nuovo per equazioni ellittiche infinito-dimensionali del secondo ordine con coefficienti Hölderiani a valori nello spazio degli operatori Hilbert-Schmidt. In particolare si mostra che la derivata seconda delle soluzioni è Hilbert-Schmidt.

Linear parabolic problems involving measures.

Herbert Amann (2001)

RACSAM

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Desarrollamos una teoría general para la resolución de ecuaciones lineales de evolución de la forma ü + Au = μ sobre R+, donde -A es el generador infinitesimal de un semigrupo analítico fuertemente continuo y μ es una medida de Radón con valores en un espacio de Banach. Utilizamos la teoría de interpolación-extrapolación de espacios y el teorema de representación de Riesz para tales medidas. Los resultados abstractos son ilustrados mediante aplicaciones...

Remarks on the powers of elliptic operators.

Jan W. Cholewa, Tomasz Dlotko (2000)

Revista Matemática Complutense

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Under natural regularity assumptions on the data the powers of regular elliptic boundary value problems (e.b.v.p.) are shown to be higher order regular e.b.v.p.. This result is used in description of the domains of fractional powers of elliptic operators which information is in order important in regularity considerations for solutions of semilinear parabolic equations. Presented approach allows to avoid C-smoothness assumption on the data that is typical in many references. ...