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On large solutions for fractional Hamilton–Jacobi equations
Published online by Cambridge University Press: 11 July 2023
Abstract
We study the existence of large solutions for nonlocal Dirichlet problems posed on a bounded, smooth domain, associated with fully nonlinear elliptic equations of order $2\,s$, with $s\in (1/2,\,1)$
, and a coercive gradient term with subcritical power $0< p<2\,s$
. Due to the nonlocal nature of the diffusion, new blow-up phenomena arise within the range $0< p<2\,s$
, involving a continuum family of solutions and/or solutions blowing-up to $-\infty$
on the boundary. This is in striking difference with the local case studied by Lasry–Lions for the subquadratic case $1< p<2$
.
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MSC classification
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- Research Article
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- Copyright
- Copyright © The Author(s), 2023. Published by Cambridge University Press on behalf of The Royal Society of Edinburgh
References
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