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Degenerate Second Order Differential Operators Generating Analytic Semigroups in L p and W 1, p
Author(s) -
Favini Angelo,
Ruiz Goldstein Giséle,
Goldstein Jerome A.,
Romanelli Silvia
Publication year - 2002
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/1522-2616(200205)238:1<78::aid-mana78>3.0.co;2-x
Subject(s) - mathematics , semigroup , order (exchange) , degenerate energy levels , differential operator , domain (mathematical analysis) , boundary (topology) , analytic semigroup , pure mathematics , boundary value problem , operator (biology) , mathematical analysis , differential (mechanical device) , discrete mathematics , biochemistry , physics , chemistry , finance , repressor , quantum mechanics , transcription factor , engineering , economics , gene , aerospace engineering
We deal with the problem of analyticity for the semigroup generated by the second order differential operator Au ≔ αu ″ + βu ′ (or by some restrictions of it) in the spaces L p (0, 1), with or without weight, and in W 1, p (0, 1), 1 < p < ∞. Here α and β are assumed real‐valued and continuous in [0, 1], with α ( x ) > 0 in (0, 1), and the domain of A is determined by the generalized Neumann boundary conditions and by Wentzell boundary conditions.