Hölder-continuity for the nonlinear stochastic heat equation with rough initial conditions

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Stoch PDE: Anal Comp (2014) 2:316–352 DOI 10.1007/s40072-014-0034-6 Hölder-continuity for the nonlinear stochastic heat equation with rough initial conditions Le Chen · Robert C. Dalang Received: 22 October 2013 / Published online: 14 August 2014 © Springer Science+Business Media New York 2014 Abstract We study space-time regularity of the solution of the nonlinear stochastic heat equation in one spatial dimension driven by space-time white noise, with a rough initial condition. This initial condition is a locally finite measure μ with, possibly, exponentially growing tails. We…

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