TY - JOUR
T1 - Fully nonlinear Hamilton–Jacobi equations of degenerate type
AU - Jesus, David
AU - Pimentel, Edgard A.
AU - Urbano, José Miguel
N1 - Funding Information:
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 ).
Funding Information:
JMU partially supported by the King Abdullah University of Science and Technology (KAUST), Saudi Arabia , by Fundação para a Ciência 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 ).
Funding Information:
DJ was supported by Fundação para a Ciência 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 ).
Publisher Copyright:
© 2022 Elsevier Ltd
PY - 2023/2
Y1 - 2023/2
N2 - 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 Lipschitz-continuous, 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.
AB - 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 Lipschitz-continuous, 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.
KW - Degenerate elliptic operators
KW - Hamilton–Jacobi equation
KW - Lipschitz regularity
KW - Two-phase free boundary problems
UR - http://www.scopus.com/inward/record.url?scp=85145570800&partnerID=8YFLogxK
U2 - 10.1016/j.na.2022.113181
DO - 10.1016/j.na.2022.113181
M3 - Article
AN - SCOPUS:85145570800
SN - 0362-546X
VL - 227
JO - Nonlinear Analysis, Theory, Methods and Applications
JF - Nonlinear Analysis, Theory, Methods and Applications
M1 - 113181
ER -