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_411_0,
author = {Enrico Priola and Lorenzo Zambotti},
title = {New optimal regularity results for infinite-dimensional elliptic equations},
journal = {Bollettino dell'Unione Matematica Italiana},
volume = {3-A},
year = {2000},
pages = {411-429},
zbl = {0959.35076},
mrnumber = {1769994},
language = {en},
url = {http://dml.mathdoc.fr/item/BUMI_2000_8_3B_2_411_0}
}
Priola, Enrico; Zambotti, Lorenzo. New optimal regularity results for infinite-dimensional elliptic equations. Bollettino dell'Unione Matematica Italiana, Tome 3-A (2000) pp. 411-429. http://gdmltest.u-ga.fr/item/BUMI_2000_8_3B_2_411_0/
[1] -, Spectral Methods in Infinite-Dimensional Analysis, Voll. 1-2, Kluwer Academic Publishers (1995). | MR 1340626 | Zbl 0832.47001
[2] -, Infinite Dimensional Elliptic Equations with Hölder continuous coefficients, Advances in Differential Equations, 1, n. 3 (1996), 425-452. | MR 1401401 | Zbl 0926.35153
[3] -, Potential Theory in Hilbert Spaces, Sympos. Appl. Math., 54, Amer. Math. Soc., Providence (1998), 27-51. | MR 1492691 | Zbl 0898.31008
[4] -, Measures and differential equations in infinite-dimensional space, Mathematics and its applications, Kluwer Academic Publishers, Dordrecht, Boston, London (1991). | MR 1140921 | Zbl 0753.46027
[5] -, On the Ornstein-Uhlenbeck operator in spaces of continuous functions, J. Funct. Anal., 131 (1995), 94-114. | MR 1343161 | Zbl 0846.47004
[6] -, Stochastic equations in infinite dimensions, Encyclopedia of Mathematics and its Applications44, Cambridge University Press (1992). | MR 1207136 | Zbl 0761.60052
[7] -, Linear operators, Part II, Interscience, New York (1958). | Zbl 0084.10402
[8] , Potential theory on Hilbert space, J. Funct. Anal., 1 (1967), 123-181. | MR 227747 | Zbl 0165.16403
[9] , Viscosity solutions of nonlinear second-order partial differential equations in Hilbert spaces, Comm. in Part. Diff. Eq., 18 (1993), 601-651. | MR 1214874 | Zbl 0812.35153
[10] --, Stochastic PDE's and Kolmogorov Equations in Infinite Dimensions, Lect. Notes in Math.1715, Springer (1999). | MR 1730228 | Zbl 0927.00037
[11] , Gaussian Measures in Banach Spaces, Lect. Notes in Math., 463, Springer Verlag (1975). | MR 461643 | Zbl 0306.28010
[12] , 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 1013931 | Zbl 0757.93084
[13] , Analytic semigroups and Optimal Regularity in Parabolic Problems, Birkhäuser, Basel (1995). | MR 1329547 | Zbl 0816.35001
[14] -, Introduction to the Theory of (Non Symmetric) Dirichlet FormsSpringer-Verlag (1992). | Zbl 0826.31001
[15] , A fundamental solution of the parabolic equation on Hilbert spaces, J. Funct. Anal., 3 (1969), 85-114. | MR 251588 | Zbl 0169.47103
[16] , Schauder estimates for a homogeneous Dirichlet problem in a half space of a Hilbert space, Nonlinear Analysis, T.M.A., to appear. | MR 1822238 | Zbl 0992.35108
[17] , Partial Differential Equations with infinitely many variables, Ph.D. Thesis. in Mathematics, Università di Milano (1999).
[18] , On a class of Markov type semigroups in spaces of uniformly continuous and bounded functions, Studia Mathematica, 136 (3) (1999), 271-295. | MR 1724248 | Zbl 0955.47024
[19] , Logarithmic Sobolev Inequalities for Gibbs States, Corso CIME, Springer-Verlag (1994). | MR 1292280 | Zbl 0801.60056
[20] , «Unbounded» second order partial differential equations in infinite dimensional Hilbert spaces, Comm. in Part. Diff. Eq., 19 (1994), 1999-2036. | MR 1301180 | Zbl 0812.35154
[21] -, Norm discontinuity of Ornstein-Uhlenbeck semigroups, Semigroup Forum, to appear. | MR 1847653 | Zbl 0960.47024
[22] , Interpolation Theory, Function spaces, Differential Operators, North-Holland, Amsterdam (1986). | MR 503903 | Zbl 0387.46032
[23] , Infinite-Dimensional Elliptic and Stochastic Equations with Hölder-Continuous Coefficients, Stochastic Anal. Appl., 17 (3) (1999), 487-508. | MR 1686963 | Zbl 0938.60051
[24] , A new approach to existence and uniqueness for martingale problems in infinite dimensions, Prob. Theory and Rel. Fields., to appear. | Zbl 0963.60059