Asymptotic Hölder regularity for the ellipsoid process
Arroyo, Á., & Parviainen, M. (2020). Asymptotic Hölder regularity for the ellipsoid process. ESAIM : Control, Optimisation and Calculus of Variations, 26, Article 112. https://doi.org/10.1051/cocv/2020034
Date
2020Copyright
© EDP Sciences, SMAI 2020
We obtain an asymptotic Hölder estimate for functions satisfying a dynamic programming principle arising from a so-called ellipsoid process. By the ellipsoid process we mean a generalization of the random walk where the next step in the process is taken inside a given space dependent ellipsoid. This stochastic process is related to elliptic equations in non-divergence form with bounded and measurable coefficients, and the regularity estimate is stable as the step size of the process converges to zero. The proof, which requires certain control on the distortion and the measure of the ellipsoids but not continuity assumption, is based on the coupling method.
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EDP SciencesISSN Search the Publication Forum
1292-8119Keywords
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https://converis.jyu.fi/converis/portal/detail/Publication/47764852
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Research Council of FinlandFunding program(s)
Academy Project, AoFAdditional information about funding
The authors have been supported by the Academy of Finland project #298641. Á. A. was partially supported by the grant MTM2017-85666-P.License
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