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We develop a solution theory in Hölder spaces for a quasi-linear stochastic PDE driven by an additive noise. The key ingredients are two deterministic PDE lemmas which establish a priori… Click to show full abstract
We develop a solution theory in Hölder spaces for a quasi-linear stochastic PDE driven by an additive noise. The key ingredients are two deterministic PDE lemmas which establish a priori Hölder bounds for a parabolic equation in divergence form with irregular right-hand-side term. We apply these bounds to the case of a right-hand-side noise term which is white in time and trace class in space, to obtain stretched exponential bounds for the Hölder semi-norms of the solution.
Keywords:
quasi linear;
spdes divergence;
divergence form;
linear spdes
Journal Title: Stochastics and Partial Differential Equations: Analysis and Computations
Year Published: 2017
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Journal Title: Stochastics and Partial Differential Equations: Analysis and Computations
Year Published: 2017
Link to full text (if available)
Share on Social Media: Sign Up to like & get
recommendations!