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The Equation u ′ + A ( t ) u = f in a Hilbert Space and L P ‐Estimates For Parabolic Equations
Author(s) -
von Wahl Wolf
Publication year - 1982
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/jlms/s2-25.3.483
Subject(s) - hilbert space , space (punctuation) , a priori and a posteriori , mathematics , a priori estimate , mathematical analysis , parabolic partial differential equation , mathematical physics , physics , partial differential equation , philosophy , linguistics , epistemology
It is the aim of this paper to present a new a priori estimate (and as a consequence an existence theorem) for solutions of u ′ + A ( t ) u = f , u (0) = Ø, in a Hilbert space. As a consequence we prove the potential theoretical L q – L 2 estimates for parabolic equations, and then all L q – L p estimates.