Elliptic and Parabolic Second-Order PDEs with Growing Coefficients
By Nicolai V. Krylov, Enrico Priola. 2008
81 citations recorded by the source corpus.
We consider a second-order parabolic equation in ℝ d+1 with possibly unbounded lower order coefficients. All coefficients are assumed to be only measurable in the time variable and locally Hölder continuous in the space variables. We show that global Schauder estimates hold even in this case. The proof introduces a new localization procedure. Our results show that the constant appearing in the classical Schauder estimates is in fact independent of the L ∞-norms of the lower order coefficients. We also give a proof of uniqueness which is of independent interest even in the case of bounded coefficients.
Subfields: Computational Theory and Mathematics, Control and Systems Engineering, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/f795087b38af7c0524d641018907e9fb240f0589
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In Computational Theory and Mathematics
- Franco Flandoli
- Massimiliano Gubinelli
- Enrico Priola
- Khoa Le
- Xicheng Zhang
- Feng-Yu Wang
- E. Fedrizzi
- Longjie Xie
In Control and Systems Engineering
- Massimiliano Gubinelli
- Franco Flandoli
- Enrico Priola
- Khoa Le
- Xicheng Zhang
- Feng-Yu Wang
- Longjie Xie
- Michael Röckner
In Mathematical Physics
- Khoa Le
- Massimiliano Gubinelli
- Enrico Priola
- Franco Flandoli
- Martin Hairer
- Samy Tindel
- Peter K. Friz
- Lucio Galeati
Citations in the corpus
- Well-posedness of the transport equation by stochastic perturbation (2008, background): “The next result deals with Schauder estimates and is known even in a more general form (see [20] and the references therein).”
- A stochastic sewing lemma and applications (2018, background): “However, unlike the cases treated in [29], a satisfactory theory for such equation is not yet available in our general setup.”