Analytic Semigroups and Optimal Regularity in Parabolic Problems
Springer Science & Business Media, 1995. jan. 1. - 424 oldal
The book shows how the abstract methods of analytic semigroups and evolution equations in Banach spaces can be fruitfully applied to the study of parabolic problems. Particular attention is paid to optimal regularity results in linear equations. Furthermore, these results are used to study several other problems, especially fully nonlinear ones. Owing to the new unified approach chosen, known theorems are presented from a novel perspective and new results are derived. The book is self-contained. It is addressed to PhD students and researchers interested in abstract evolution equations and in parabolic partial differential equations and systems. It gives a comprehensive overview on the present state of the art in the field, teaching at the same time how to exploit its basic techniques.
Mit mondanak mások - Írjon ismertetőt
Nem találtunk ismertetőket a szokott helyeken.
spaces of continuous
Analytic semigroups and intermediate spaces
Generation of analytic semigroups by elliptic operators
Linear parabolic problems
Linear nonautonomous equations
A G C asymptotically stable Au(t Banach space belongs to C([0 boundary condition bounded functions bounded with values C D(A C(Rn C2m boundary classical solution coefficients consider constant continuous and bounded continuous functions continuous with values continuously differentiable continuously embedded Corollary Da(a DA(a,oo derivatives Dirichlet boundary condition eigenvalue elliptic elliptic operator equations equivalent etAx exists fixed point fully nonlinear Holder continuous Holder spaces holds implies initial datum interpolation spaces interval l,oo Lemma Let f Let us prove linear operator Lipschitz continuous mild solution Moreover null solution open set priori estimates proof of Theorem regularity properties Reiteration Theorem replaced resolvent set second order Section sectorial operator semigroup set in Rn solution of 4.0.1 spectral set stability statement follows strict solution strong solution Subsection T-periodic thanks to Proposition uniformly C2 uniformly continuous unique solution values in D(A