Abstract
The existence of martingale solutions for stochastic porous media equations driven by nonlinear multiplicative space–time white noise is established in spatial dimension one. The Stroock–Varopoulos inequality is identified as a key tool in the derivation of the corresponding estimates.
L’existence d’une solution martingale pour l’équation stochastique des milieux poreux, dirigée par un bruit non-linéaire multiplicatif en espace et en temps, est établie dans le cas spatial unidimensionnel. L’inégalité de Stroock–Varopoulos est identifiée comme un outil clé dans l’obtention des estimées correspondantes.
Acknowledgements
BG acknowledges financial support by the DFG through the CRC 1283 “Taming uncertainty and profiting from randomness and low regularity in analysis, stochastics and their applications”. MG thanks the support of the Austrian Science Fund (FWF) through the Lise Meitner programme M2250-N32. The authors thank the anonymous referee for their numerous suggestions on improving the presentation of the paper.
Citation
K. Dareiotis. M. Gerencsér. B. Gess. "Porous media equations with multiplicative space–time white noise." Ann. Inst. H. Poincaré Probab. Statist. 57 (4) 2354 - 2371, November 2021. https://doi.org/10.1214/20-AIHP1139
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