Regularity of the solutions to SPDEs in metric measure spaces
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Publication:744877
DOI10.1007/S40072-015-0048-8zbMATH Open1323.60084arXiv1409.3399OpenAlexW3100521324WikidataQ59897096 ScholiaQ59897096MaRDI QIDQ744877
Author name not available (Why is that?)
Publication date: 12 October 2015
Published in: (Search for Journal in Brave)
Abstract: In this paper we study the regularity of non-linear parabolic PDEs and stochastic PDEs on metric measure spaces admitting heat kernels. In particular we consider mild function solutions to abstract Cauchy problems and show that the unique solution is H"older continuous in time with values in a suitable fractional Sobolev space. As this analysis is done via a-priori estimates, we can apply this result to stochastic PDEs on metric measure spaces and solve the equation in a pathwise sense for almost all paths. The main example of noise term is of fractional Brownian type and the metric measure spaces can be classical as well as given by various fractal structures. The whole approach is low dimensional and works for spectral dimensions less than 4.
Full work available at URL: https://arxiv.org/abs/1409.3399
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