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Referenza completa

Da Prato, Giuseppe:
Some results on elliptic and parabolic equations in Hilbert spaces (Equazioni ellittiche e paraboliche negli spazi di Hilbert)
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni Serie 9 7 (1996), fasc. n.3, p. 181-199, (English)
pdf (1.46 MB), djvu (396 Kb). | MR1454413 | Zbl 0881.47018

Sunto

In questo lavoro si considerano equazioni ellittiche e paraboliche con un numero finito di variabili. Si provano risultati di esistenza, unicità e regolarità delle soluzioni.
Referenze Bibliografiche
[1] P. CANNARSA - G. DA PRATO, On a functional analysis approach to parabolic equations in infinite dimensions. J. Funct. Anal., 118, 1, 1993, 22-42. | fulltext (doi) | MR 1245596 | Zbl 0787.35115
[2] P. CANNARSA - G. DA PRATO, Infinite dimensional elliptic equations with Hölder continuous coefficients. Advances in Differential Equations, 1, 3, 1996, 425-452. | MR 1401401 | Zbl 0926.35153
[3] P. CANNARSA - G. DA PRATO, Schauder estimates for Kolmogorov equations in Hilbert spaces. Proceedings of the meeting on Elliptic and Parabolic PDE's and Applications (Capri, September 1994). To appear. | MR 1430142 | Zbl 0890.35159
[4] S. CERRAI, A Hille-Yosida Theorem for weakly continuous semigroups. Semigroup Forum, 49, 1994, 349-367 | fulltext EuDML | fulltext (doi) | MR 1293091 | Zbl 0817.47048
[5] S. CERRAI - F. GOZZI, Strong solutions of Cauchy problems associated to weakly continuous semigroups. Differential and Integral Equations, 8, 3, 1994, 465-486. | MR 1306569 | Zbl 0822.47040
[6] G. DA PRATO, Transition semigroups associated with Kolmogorov equations in Hilbert spaces. In: M. CHIPOT - J. SAINT JEAN PAULIN - I. SHAFRIR (eds.), Progress in Partial Differential Equations: the Metz Surveys 3. Pitman Research Notes in Mathematics Series, no. 314, 1994, 199-214. | MR 1316200 | Zbl 0908.47034
[7] G. DA PRATO - A. LUNARDI, On the Ornstein-Uhlenbeck operator in spaces of continuous functions. J. Funct. Anal., 131, 1995, 94-114. | fulltext (doi) | MR 1343161 | Zbl 0846.47004
[8] G. DA PRATO - J. ZABCZYK, Stochastic equations in infinite dimensions. Encyclopedia of Mathematics and its Applications, Cambridge University Press, 1992. | fulltext (doi) | MR 1207136 | Zbl 0761.60052
[9] JU. L. DALECKIJ, Differential equations with functional derivatives and stochastic equations for generalized random processes. Dokl. Akad. Nauk SSSR, 166, 1966, 1035-1038. | MR 214943 | Zbl 0305.35084
[10] N. DUNFORD - J. T. SCHWARTZ, Linear Operators. Vol. II, 1956. | Zbl 0084.10402
[11] L. GROSS, Potential Theory in Hilbert spaces. J. Funct. Anal., 1, 1965, 139-189. | Zbl 0165.16403
[12] H. H. KUO, Gaussian Measures in Banach Spaces. Springer-Verlag, 1975. | MR 461643 | Zbl 0306.28010
[13] J. M. LASRY - P. L. LIONS, A remark on regularization in Hilbert spaces. Israel J. Math., 55, 3, 1986, 257-266. | fulltext (doi) | MR 876394 | Zbl 0631.49018
[14] J. L. LIONS - J. PEETRE, Sur une classe d'espaces d'interpolation. Publ. Math. de l'I.H.E.S., 19, 1964, 5-68. | fulltext EuDML | fulltext mini-dml | MR 165343 | Zbl 0148.11403
[15] A. LUNARDI, Analytic Semigroups and Optimal Regularity in Parabolic Problems. Birkhäuser Verlag, Basel 1995. | fulltext (doi) | MR 1329547 | Zbl 0816.35001
[16] A. LUNARDI, An interpolation method to characterize domains of generators of semigroups. Semigroup Forum, to appear. | fulltext EuDML | fulltext (doi) | MR 1406778 | Zbl 0859.47030
[17] A. S. NEMIROVKI - S. M. SEMENOV, The polynomial approximation of functions in Hilbert spaces. Mat. Sb. (N.S.), 92, 134, 1973, 257-281. | MR 632033 | Zbl 0286.41025
[18] A. PIECH, Regularity of the Greens operator in Abstract Wiener Space. J. Diff. Eq., 12, 1969, 353-360. | Zbl 0228.47034
[19] A. PIECH, A fundamental solution of the parabolic equation on Hilbert space. J. Funct. Anal., 3, 1972, 85-114. | Zbl 0169.47103
[20] H. TRIEBEL, Interpolation Theory, Function Spaces, Differential Operators. North-Holland, Amsterdam 1986. | MR 503903 | Zbl 0387.46032

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