Summary
Sia A il generatore di un semigruppo analitico in uno spazio di Banach. In questo lavoro si studia in modo sistematico la regolarità delle soluzioni dell'equazione parabolica astratta u′(t)=Au(t)+f(t), u(0)=u 0,in funzione della regolarità dei fati f e u0.
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References
A. Adams,Sobolev spaces, Academic Press, New York (1975).
S. Agmon,On the eigenfunctions and on the eigenvalues of general elliptic boundary value problems, Comm. Pure Appl. Math.,15 (1962), pp. 119–147.
H.Amann,Dual semigroups and second order linear elliptic boundary value problems, Israel J. Math. (to appear).
P.L. Butzer -H. Berens,Semigroups of operators and approximation, Springer, Berlin (1967).
G. Da Prato,Applications croissantes et équations d'évolution dans les espaces de Banach, Academic Press, New York (1976).
G. Da Prato -P. Grisvard,Sommes d'opérateurs linéaires et équations différentielles opérationnelles, J. Math. Pures Appl.,54 (1975), pp. 305–387.
L. De Simon,Un'applicazione della teoria degli integrali singolari allo studio delle equazioni differenziali lineari astratte del primo ordine, Rend. Sem. Mat. Padova,34 (1964), pp. 205–232.
P. Grisvard,Commutativité de deux foncteurs d'interpolation et applications, J. Math. Pures Appl.,45 (1966), pp. 207–290.
P. Grisvard,Equations différentielles abstraites, Ann. Scient. Ec. Norm. Sup.,2 (1969), pp. 311–395.
P. Grisvard,Boundary value problems in non smooth domains, Lecture Notes, University of Maryland, College Park (1980).
T. Kato,Perturbation theory for linear operators, Springer, Berlin (1966).
O. A. Ladyzenskaja -V. A. Solonnikov -N. N. Uralceva,Linear and quasilinear equations of parabolic type, Amer. Math. Soc., Providence (1968).
J. L. Lions,Théorèmes de trace et d'interpolation (I), Ann. Sc. Norm. Pisa,13 (1959), pp. 389–403.
J. L. Lions -E. Magenes,Problèmes aux limites non homogenes et applications, Dunod, Paris (1968).
W. Von Wahl,The equation u′+A(t)u=f in a Hilbert space and L p-estimates for parabolic equations, J. London Math. Soc.,25 (1982), pp. 483–497.
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Work done under the auspices of the G.N.A.F.A. of the C.N.R.
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Di Blasio, G. Linear parabolic evolution equations inL p-spaces. Annali di Matematica pura ed applicata 138, 55–104 (1984). https://doi.org/10.1007/BF01762539
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DOI: https://doi.org/10.1007/BF01762539