Some results for pathwise uniqueness in Hilbert spaces

Giuseppe Da Prato; Franco Flandoli

doi:10.3934/cpaa.2014.13.1789

Article Contents

2014, Volume 13, Issue 5: 1789-1797. Doi: 10.3934/cpaa.2014.13.1789

This issue Previous Article Multiple Jacobian equations Next Article On the free boundary for quenching type parabolic problems via local energy methods

Some results for pathwise uniqueness in Hilbert spaces

Giuseppe Da Prato^1, and
Franco Flandoli^2,

1.
Scuola Normale Superiore, Piazza dei Cavalieri 6, 56126 Pisa
2.
Dipartimento di Matematica Applicata, "U.Dini" Università di Pisa, V.le B. Pisano 26/b, 56126 Pisa

Received: August 31, 2013

Revised: February 28, 2014

Published: August 2015

Abstract Related Papers Cited by

Abstract

An abstract evolution equation in Hilbert spaces with Hölder continuous drift is considered. By proceeding as in [3], we transform the equation in another equation with Lipschitz continuous coefficients.Then we prove existence and uniqueness of this equation by a fixed point argument.

Keywords:

Mathematics Subject Classification: 35R60, 60H15.

Citation:

Related Papers

Cited by

References

[1]	S. Cerrai, A Hille-Yosida theorem for weakly continuous semigroups, Semigroup Forum, 49 (1994), 349-367.doi: 10.1007/BF02573496.
[2]	G. Da Prato and J. Zabczyk, Second Order Partial Differential Equations in Hilbert Spaces, London Mathematical Society, Lecture Notes 293, Cambridge University Press, 2002.doi: 10.1017/CBO9780511543210.
[3]	G. Da Prato and F. Flandoli, Pathwise uniqueness for a class of SDE in Hilbert spaces and applications, J. Funct. Anal., 259 (2010), 243-267.doi: 10.1016/j.jfa.2009.11.019.
[4]	F. Flandoli, Random perturbation of PDEs and fluid dynamic models, Lecture Notes in Mathematics, 2015, Springer, Berlin, 2011.doi: 10.1007/978-3-642-18231-0.
[5]	J. M. Lasry and P. L. Lions, A remark on regularization in Hilbert spaces, Israel J. Math., 55 (1986), 257-266.doi: 10.1007/BF02765025.
[6]	J. L. Lions and E. Magenes, Problèmes aux limites non homogènes et applications, Dunod, 1968.
[7]	M. Ondreját, Uniqueness for Stochastic Evolution Equations in Banach Spaces, Dissertationes Math. (Rozprawy Mat.), no. 426, 2004.doi: 10.4064/dm426-0-1.
[8]	M. Röckner, B. Schmuland and X. Zhang, The Yamada-Watanabe theorem for stochastic evolution equations in infinite dimensions, Comm. Mat. Phys., 11 (2008), 247-259.
[9]	H. Triebel, Interpolation Theory, Function Spaces, Differential Operators, North-Holland, 1978.