A note on second derivative estimates for Monge-Ampe`re type equations

DOI10.1515/ANS-2022-0036zbMATH Open1517.35116arXiv2204.01039MaRDI QIDQ6395515

Publication date: 3 April 2022

Abstract: In this note we revisit previous Pogorelov type interior and global second derivative estimates of the author, F. Jiang and J. Liu for solutions of Monge-Amp`ere type partial differential equations. Taking account of recent strict convexity regularity results of Guillen, Kitagawa and Rankin, and following our earlier work in the optimal transportation case, we remove the monotonicity assumptions in the more general case of generated Jacobian equations and consequently in the subsequent application to classical solvability and global regularity for second boundary value problems.

Mathematics Subject Classification ID

Transportation, logistics and supply chain management (90B06) Geometric optics (78A05) Monge-Ampère equations (35J96)

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