$L^p$-Theory for Elliptic Operators on $\mathbb R^d$ with Singular Coefficients | Zendy

Giorgio Metafune | Zendy; Diego Pallara | Zendy; Jan Prüß | Zendy; Roland Schnaubelt | Zendy

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$L^p$-Theory for Elliptic Operators on $\mathbb R^d$ with Singular Coefficients

Author(s) -

Giorgio Metafune,

Diego Pallara,

Jan Prüß,

Roland Schnaubelt

Publication year - 2005

Publication title -

zeitschrift für analysis und ihre anwendungen

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.567

H-Index - 35

eISSN - 1661-4534

pISSN - 0232-2064

DOI - 10.4171/zaa/1253

Subject(s) - mathematics , bounded function , elliptic operator , semigroup , gravitational singularity , order (exchange) , analytic semigroup , domain (mathematical analysis) , pure mathematics , mathematical analysis , half period ratio , type (biology) , class (philosophy) , quarter period , elliptic curve , nome , ecology , finance , artificial intelligence , computer science , economics , biology

We study the generation of an analytic semigroup in Lp(Rd) and the de- termination of the domain for a class of second order elliptic operators with unbounded coecien ts in Rd. We also establish the maximal regularity of type Lq{Lp for the corre- sponding inhomogeneous parabolic equation. In contrast to the previous literature the coecien ts of the second derivatives are not required to be strictly elliptic or bounded. Interior singularities of the lower order terms are also discussed.

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