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https://hdl.handle.net/10316/114115| Title: | Fully nonlinear Hamilton–Jacobi equations of degenerate type | Authors: | Jesus, David Pimentel, Edgard A. Urbano, José Miguel |
Keywords: | Degenerate elliptic operators; Hamilton–Jacobi equation; Lipschitz regularity; Two-phase free boundary problems | Issue Date: | 2023 | Publisher: | Elsevier | Project: | DJ was supported by Funda¸c˜ao para a Ciˆencia e a Tecnologia, Portugal, through scholarship PD/BD/150354/2019, under POCH funds, co-financed by the European Social Fund and Portuguese National Funds from MCTES, and by the Centre for Mathematics of the University of Coimbra, Portugal (UIDB/00324/2020, funded by the Portuguese Government through FCT/MCTES). EP partially supported by the Centre for Mathematics of the University of Coimbra (UIDB/00324/2020, funded by the Portuguese Government through FCT/MCTES) and by FAPERJ (grants E26/200.002/2018 and E26/201.390/2021). JMU partially supported by the King Abdullah University of Science and Technology (KAUST), Saudi Arabia, by Funda¸c˜ao para a Ciˆencia e a Tecnologia, through project PTDC/MAT-PUR/28686/2017, and by the Centre for Mathematics of the University of Coimbra (UIDB/00324/2020, funded by the Portuguese Government through FCT/MCTES). | Serial title, monograph or event: | Nonlinear Analysis, Theory, Methods and Applications | Volume: | 227 | Abstract: | We examine Hamilton–Jacobi equations driven by fully nonlinear degenerate elliptic operators in the presence of superlinear Hamiltonians. By exploring the Ishii–Jensen inequality, we prove that viscosity solutions are locally Lipschitzcontinuous, with estimates depending on the structural conditions of the problem. We close the paper with an application of our findings to a two-phase free boundary problem. | URI: | https://hdl.handle.net/10316/114115 | ISSN: | 0362546X | DOI: | 10.1016/j.na.2022.113181 | Rights: | openAccess |
| Appears in Collections: | I&D CMUC - Artigos em Revistas Internacionais FCTUC Matemática - Artigos em Revistas Internacionais |
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| Fully nonlinear Hamilton–Jacobi equations of degenerate type.pdf | 745.1 kB | Adobe PDF | View/Open |
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