Some results on elliptic and parabolic equations in Hilbert spaces

Giuseppe Da Prato

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni (1996)

  • Volume: 7, Issue: 3, page 181-199
  • ISSN: 1120-6330

Abstract

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We consider elliptic and parabolic equations with infinitely many variables. We prove some results of existence, uniqueness and regularity of solutions.

How to cite

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Da Prato, Giuseppe. "Some results on elliptic and parabolic equations in Hilbert spaces." Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni 7.3 (1996): 181-199. <http://eudml.org/doc/244148>.

@article{DaPrato1996,
abstract = {We consider elliptic and parabolic equations with infinitely many variables. We prove some results of existence, uniqueness and regularity of solutions.},
author = {Da Prato, Giuseppe},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
keywords = {Elliptic and parabolic equations in Hilbert spaces; Ornstein-Uhlenbeck semigroup; Schauder estimates; elliptic and parabolic equations; infinitely many variables; existence; uniqueness; regularity of solutions},
language = {eng},
month = {12},
number = {3},
pages = {181-199},
publisher = {Accademia Nazionale dei Lincei},
title = {Some results on elliptic and parabolic equations in Hilbert spaces},
url = {http://eudml.org/doc/244148},
volume = {7},
year = {1996},
}

TY - JOUR
AU - Da Prato, Giuseppe
TI - Some results on elliptic and parabolic equations in Hilbert spaces
JO - Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
DA - 1996/12//
PB - Accademia Nazionale dei Lincei
VL - 7
IS - 3
SP - 181
EP - 199
AB - We consider elliptic and parabolic equations with infinitely many variables. We prove some results of existence, uniqueness and regularity of solutions.
LA - eng
KW - Elliptic and parabolic equations in Hilbert spaces; Ornstein-Uhlenbeck semigroup; Schauder estimates; elliptic and parabolic equations; infinitely many variables; existence; uniqueness; regularity of solutions
UR - http://eudml.org/doc/244148
ER -

References

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  1. CANNARSA, P. - DA PRATO, G., On a functional analysis approach to parabolic equations in infinite dimensions. J. Funct. Anal., 118, 1, 1993, 22-42. Zbl0787.35115MR1245596DOI10.1006/jfan.1993.1137
  2. CANNARSA, P. - DA PRATO, G., Infinite dimensional elliptic equations with Hölder continuous coefficients. Advances in Differential Equations, 1, 3, 1996, 425-452. Zbl0926.35153MR1401401
  3. CANNARSA, P. - DA PRATO, G., 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. Zbl0890.35159MR1430142
  4. CERRAI, S., A Hille-Yosida Theorem for weakly continuous semigroups. Semigroup Forum, 49, 1994, 349-367 Zbl0817.47048MR1293091DOI10.1007/BF02573496
  5. CERRAI, S. - GOZZI, F., Strong solutions of Cauchy problems associated to weakly continuous semigroups. Differential and Integral Equations, 8, 3, 1994, 465-486. Zbl0822.47040MR1306569
  6. DA PRATO, G., 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. Zbl0908.47034MR1316200
  7. DA PRATO, G. - LUNARDI, A., On the Ornstein-Uhlenbeck operator in spaces of continuous functions. J. Funct. Anal., 131, 1995, 94-114. Zbl0846.47004MR1343161DOI10.1006/jfan.1995.1084
  8. DA PRATO, G. - ZABCZYK, J., Stochastic equations in infinite dimensions. Encyclopedia of Mathematics and its Applications, Cambridge University Press, 1992. Zbl0761.60052MR1207136DOI10.1017/CBO9780511666223
  9. DALECKIJ, JU. L., Differential equations with functional derivatives and stochastic equations for generalized random processes. Dokl. Akad. Nauk SSSR, 166, 1966, 1035-1038. Zbl0305.35084MR214943
  10. DUNFORD, N. - SCHWARTZ, J. T., Linear Operators. Vol. II, 1956. Zbl0084.10402
  11. GROSS, L., Potential Theory in Hilbert spaces. J. Funct. Anal., 1, 1965, 139-189. Zbl0165.16403
  12. KUO, H. H., Gaussian Measures in Banach Spaces. Springer-Verlag, 1975. Zbl0306.28010MR461643
  13. LASRY, J. M. - LIONS, P. L., A remark on regularization in Hilbert spaces. Israel J. Math., 55, 3, 1986, 257-266. Zbl0631.49018MR876394DOI10.1007/BF02765025
  14. LIONS, J. L. - PEETRE, J., Sur une classe d'espaces d'interpolation. Publ. Math. de l'I.H.E.S., 19, 1964, 5-68. Zbl0148.11403MR165343
  15. LUNARDI, A., Analytic Semigroups and Optimal Regularity in Parabolic Problems. Birkhäuser Verlag, Basel1995. Zbl0816.35001MR1329547DOI10.1007/978-3-0348-9234-6
  16. LUNARDI, A., An interpolation method to characterize domains of generators of semigroups. Semigroup Forum, to appear. Zbl0859.47030MR1406778DOI10.1007/BF02574147
  17. NEMIROVKI, A. S. - SEMENOV, S. M., The polynomial approximation of functions in Hilbert spaces. Mat. Sb. (N.S.), 92, 134, 1973, 257-281. Zbl0286.41025MR632033
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  20. TRIEBEL, H., Interpolation Theory, Function Spaces, Differential Operators. North-Holland, Amsterdam1986. Zbl0387.46032MR503903

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