{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T14:05:28Z","timestamp":1787321128327,"version":"build-2736575974"},"reference-count":23,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"4","funder":[{"name":"Early Career Scientists","award":["19K14564"],"award-info":[{"award-number":["19K14564"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Math. Anal."],"published-print":{"date-parts":[[2023,8,31]]},"abstract":"<jats:p>Abstract.<\/jats:p>\n                  <jats:p>We present a new approach to deriving lower bounds for weak spatial gradients of a viscosity solution to a Hamilton\u2013Jacobi equation when the Hamiltonian is convex. For the proof, we consider Hamiltonian systems with approximate Hamiltonians and study how the initial gradients propagate along the solutions to the Hamiltonian systems. We also apply our method to the case of homogeneous Hamiltonians, whose examples include level-set equations arising in surface evolution problems. In this case we obtain sharper gradient estimates. Moreover, we compare our results with the previous work [O. Ley, Adv. Differential Equations, 6 (2001), pp. 547\u2013576]. We show that our results give better and optimal estimates in several senses.<\/jats:p>","DOI":"10.1137\/22m1480483","type":"journal-article","created":{"date-parts":[[2023,7,28]],"date-time":"2023-07-28T04:22:12Z","timestamp":1690518132000},"page":"3169-3204","source":"Crossref","is-referenced-by-count":1,"title":["A Dynamical Approach to Lower Gradient Estimates for Viscosity Solutions of Hamilton\u2013Jacobi Equations"],"prefix":"10.1137","volume":"55","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-9556-5052","authenticated-orcid":true,"given":"Nao","family":"Hamamuki","sequence":"first","affiliation":[{"name":"Department of Mathematics, Faculty of Science, Hokkaido University, Hokkaido 060-0808, Japan."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Kazuya","family":"Hirose","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Graduate School of Science, Hokkaido University, Hokkaido 060-0808, Japan."}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2023,7,28]]},"reference":[{"key":"ref1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-36433-4"},{"key":"ref2","doi-asserted-by":"publisher","DOI":"10.1016\/j.jde.2019.08.051"},{"key":"ref3","volume-title":"Optimal Control and Viscosity Solutions of Hamilton-Jacobi-Bellman Equations, Systems Control Found. 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