STOCHASTIC VARIATIONAL INEQUALITIES AND REGULARITY FOR DEGENERATE STOCHASTIC PARTIAL DIFFERENTIAL EQUATIONS

Gess B, Röckner M (2017)
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY 369(5): 3017-3045.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
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Abstract / Bemerkung
The regularity and characterization of solutions to degenerate, quasilinear SPDE is studied. Our results are two-fold: First, we prove regularity results for solutions to certain degenerate, quasilinear SPDE driven by Lipschitz continuous noise. In particular, this provides a characterization of solutions to such SPDE in terms of (generalized) strong solutions. Second, for the one-dimensional stochastic mean curvature flow with normal noise we adapt the notion of stochastic variational inequalities to provide a characterization of solutions previously obtained in a limiting sense only. This solves a problem left open by A. Es-Sarhir and M.-K. von Renesse in 2012 and sharpens regularity properties obtained by them with W. Stannat.
Stichworte
Degenerate SPDE; degenerate p-Laplace; mean curvature flow; regularity; stochastic variational inequalities; linear growth functionals
Erscheinungsjahr
2017
Zeitschriftentitel
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY
Band
369
Ausgabe
5
Seite(n)
3017-3045
ISSN
0002-9947
eISSN
1088-6850
Page URI
https://pub.uni-bielefeld.de/record/2910486

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Gess B, Röckner M. STOCHASTIC VARIATIONAL INEQUALITIES AND REGULARITY FOR DEGENERATE STOCHASTIC PARTIAL DIFFERENTIAL EQUATIONS. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY. 2017;369(5):3017-3045.
Gess, B., & Röckner, M. (2017). STOCHASTIC VARIATIONAL INEQUALITIES AND REGULARITY FOR DEGENERATE STOCHASTIC PARTIAL DIFFERENTIAL EQUATIONS. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 369(5), 3017-3045. doi:10.1090/tran/6981
Gess, B., and Röckner, M. (2017). STOCHASTIC VARIATIONAL INEQUALITIES AND REGULARITY FOR DEGENERATE STOCHASTIC PARTIAL DIFFERENTIAL EQUATIONS. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY 369, 3017-3045.
Gess, B., & Röckner, M., 2017. STOCHASTIC VARIATIONAL INEQUALITIES AND REGULARITY FOR DEGENERATE STOCHASTIC PARTIAL DIFFERENTIAL EQUATIONS. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 369(5), p 3017-3045.
B. Gess and M. Röckner, “STOCHASTIC VARIATIONAL INEQUALITIES AND REGULARITY FOR DEGENERATE STOCHASTIC PARTIAL DIFFERENTIAL EQUATIONS”, TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, vol. 369, 2017, pp. 3017-3045.
Gess, B., Röckner, M.: STOCHASTIC VARIATIONAL INEQUALITIES AND REGULARITY FOR DEGENERATE STOCHASTIC PARTIAL DIFFERENTIAL EQUATIONS. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY. 369, 3017-3045 (2017).
Gess, Benjamin, and Röckner, Michael. “STOCHASTIC VARIATIONAL INEQUALITIES AND REGULARITY FOR DEGENERATE STOCHASTIC PARTIAL DIFFERENTIAL EQUATIONS”. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY 369.5 (2017): 3017-3045.

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