Geodesic
New optimal regularity results for infinite-dimensional elliptic equations
Bollettino della Unione matematica italiana, Série 8, 3B (2000) no. 2, pp. 411-429.

Voir la notice de l'article provenant de la source Biblioteca Digitale Italiana di Matematica

In questo articolo si ottengono stime di Schauder di tipo nuovo per equazioni ellittiche infinito-dimensionali del secondo ordine con coefficienti Hölderiani a valori nello spazio degli operatori Hilbert-Schmidt. In particolare si mostra che la derivata seconda delle soluzioni è Hilbert-Schmidt. 
@article{BUMI_2000_8_3B_2_a9,
     author = {Priola, Enrico and Zambotti, Lorenzo},
     title = {New optimal regularity results for infinite-dimensional elliptic equations},
     journal = {Bollettino della Unione matematica italiana},
     pages = {411--429},
     publisher = {mathdoc},
     volume = {Ser. 8, 3B},
     number = {2},
     year = {2000},
     zbl = {0959.35076},
     mrnumber = {1340626},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/BUMI_2000_8_3B_2_a9/}
}
TY  - JOUR
AU  - Priola, Enrico
AU  - Zambotti, Lorenzo
TI  - New optimal regularity results for infinite-dimensional elliptic equations
JO  - Bollettino della Unione matematica italiana
PY  - 2000
SP  - 411
EP  - 429
VL  - 3B
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/BUMI_2000_8_3B_2_a9/
LA  - en
ID  - BUMI_2000_8_3B_2_a9
ER  - 
%0 Journal Article
%A Priola, Enrico
%A Zambotti, Lorenzo
%T New optimal regularity results for infinite-dimensional elliptic equations
%J Bollettino della Unione matematica italiana
%D 2000
%P 411-429
%V 3B
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/BUMI_2000_8_3B_2_a9/
%G en
%F BUMI_2000_8_3B_2_a9
Priola, Enrico; Zambotti, Lorenzo. New optimal regularity results for infinite-dimensional elliptic equations. Bollettino della Unione matematica italiana, Série 8, 3B (2000) no. 2, pp. 411-429. http://geodesic.mathdoc.fr/item/BUMI_2000_8_3B_2_a9/

[1] Y. M. Bererezansky-Y. G. Kondratiev, Spectral Methods in Infinite-Dimensional Analysis, Voll. 1-2, Kluwer Academic Publishers (1995). | MR | Zbl

[2] P. Cannarsa-G. Da Prato, Infinite Dimensional Elliptic Equations with Hölder continuous coefficients, Advances in Differential Equations, 1, n. 3 (1996), 425-452. | MR | Zbl

[3] P. Cannarsa-G. Da Prato, Potential Theory in Hilbert Spaces, Sympos. Appl. Math., 54, Amer. Math. Soc., Providence (1998), 27-51. | MR | Zbl

[4] Y. L. Dalecky-S. V. Fomin, Measures and differential equations in infinite-dimensional space, Mathematics and its applications, Kluwer Academic Publishers, Dordrecht, Boston, London (1991). | MR | Zbl

[5] G. Da Prato-A. Lunardi, On the Ornstein-Uhlenbeck operator in spaces of continuous functions, J. Funct. Anal., 131 (1995), 94-114. | MR | Zbl

[6] G. Da Prato-J. Zabczyk, Stochastic equations in infinite dimensions, Encyclopedia of Mathematics and its Applications 44, Cambridge University Press (1992). | MR | Zbl

[7] N. Dunford-J. Schwartz, Linear operators, Part II, Interscience, New York (1958). | Zbl

[8] L. Gross, Potential theory on Hilbert space, J. Funct. Anal., 1 (1967), 123-181. | MR | Zbl

[9] H. Ishii, Viscosity solutions of nonlinear second-order partial differential equations in Hilbert spaces, Comm. in Part. Diff. Eq., 18 (1993), 601-651. | MR | Zbl

[10] N. V. Krylov-M. Röckner-J. Zabczyk, Stochastic PDE's and Kolmogorov Equations in Infinite Dimensions, Lect. Notes in Math. 1715, Springer (1999). | MR | Zbl

[11] H. H. Kuo, Gaussian Measures in Banach Spaces, Lect. Notes in Math., 463, Springer Verlag (1975). | MR | Zbl

[12] P. L. Lions, Viscosity Solutions of fully nonlinear second-order equations and optimal stochastic control in infinite-dimentions. Part III. Uniqueness of viscosity solutions of general second order equations, J. Funct. Anal., 86 (1989), 1-18. | MR | Zbl

[13] A. Lunardi, Analytic semigroups and Optimal Regularity in Parabolic Problems, Birkhäuser, Basel (1995). | MR | Zbl

[14] Z. M. Ma-M. Rockner, Introduction to the Theory of (Non Symmetric) Dirichlet Forms Springer-Verlag (1992). | Zbl

[15] A. Piech, A fundamental solution of the parabolic equation on Hilbert spaces, J. Funct. Anal., 3 (1969), 85-114. | MR | Zbl

[16] E. Priola, Schauder estimates for a homogeneous Dirichlet problem in a half space of a Hilbert space, Nonlinear Analysis, T.M.A., to appear. | MR | Zbl

[17] E. Priola, Partial Differential Equations with infinitely many variables, Ph.D. Thesis. in Mathematics, Università di Milano (1999).

[18] E. Priola, On a class of Markov type semigroups in spaces of uniformly continuous and bounded functions, Studia Mathematica, 136 (3) (1999), 271-295. | fulltext mini-dml | MR | Zbl

[19] D. W. Stroock, Logarithmic Sobolev Inequalities for Gibbs States, Corso CIME, Springer-Verlag (1994). | MR | Zbl

[20] A. Swiech, «Unbounded» second order partial differential equations in infinite dimensional Hilbert spaces, Comm. in Part. Diff. Eq., 19 (1994), 1999-2036. | MR | Zbl

[21] J. M. A. M. Van Neerven-J. Zabczyk, Norm discontinuity of Ornstein-Uhlenbeck semigroups, Semigroup Forum, to appear. | MR | Zbl

[22] H. Triebel, Interpolation Theory, Function spaces, Differential Operators, North-Holland, Amsterdam (1986). | MR | Zbl

[23] L. Zambotti, Infinite-Dimensional Elliptic and Stochastic Equations with Hölder-Continuous Coefficients, Stochastic Anal. Appl., 17 (3) (1999), 487-508. | MR | Zbl

[24] L. Zambotti, A new approach to existence and uniqueness for martingale problems in infinite dimensions, Prob. Theory and Rel. Fields., to appear. | Zbl