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We prove an asymptotic Lipschitz estimate for value functions of tug-of-war games with varying probabilities defined in Ω ? ?n. The method of the proof is based on a game-theoretic idea to estimate the value of a related game defined in Ω ×Ω via couplings.
相似文献2.
Hannes Luiro 《Israel Journal of Mathematics》2014,199(1):267-286
We study the regularity properties of the Hamilton-Jacobi flow equation and infimal convolution in the case where the initial datum function is continuous and lies in a given Sobolev-space W 1,p (? n ). We prove that under suitable assumptions it holds for solutions w(x, t) that D x w(·, t) → Du(·) in L p (? n ) as t → 0. Moreover, we construct examples showing that our results are essentially optimal. 相似文献
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Hannes Luiro 《Proceedings of the American Mathematical Society》2007,135(1):243-251
We establish the continuity of the Hardy-Littlewood maximal operator on Sobolev spaces , . As an auxiliary tool we prove an explicit formula for the derivative of the maximal function.
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Hannes Luiro Mikko Parviainen 《Annales de l'Institut Henri Poincaré (C) Analyse Non Linéaire》2018,35(6):1435-1456
We establish regularity for functions satisfying a dynamic programming equation, which may arise for example from stochastic games or discretization schemes. Our results can also be utilized in obtaining regularity and existence results for the corresponding partial differential equations. 相似文献
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We obtain (essentially sharp) boundedness results for certain generalized local maximal operators between fractional weighted Sobolev spaces and their modifications. Concrete boundedness results between well known fractional Sobolev spaces are derived as consequences of our main result. We also apply our boundedness results by studying both generalized neighbourhood capacities and the Lebesgue differentiation of fractional weighted Sobolev functions. 相似文献
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We give a proof of asymptotic Lipschitz continuity of p-harmonious functions, that are tug-of-war game analogies of ordinary p-harmonic functions. This result is used to obtain a new proof of Lipschitz continuity and Harnack's inequality for p-harmonic functions in the case p > 2. The proof avoids classical techniques like Moser iteration, but instead relies on suitable choices of strategies for the stochastic tug-of-war game. 相似文献
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