Comparison principles for nonlocal Hamilton-Jacobi equations
نویسندگان
چکیده
<p style='text-indent:20px;'>We prove the comparison principle for viscosity sub and super solutions of degenerate nonlocal operators with general gradient nonlinearities. The proofs apply to purely Hamilton-Jacobi equations order <inline-formula><tex-math id="M1">\begin{document}$ 0&lt;s&lt;1 $\end{document}</tex-math></inline-formula>.</p>
منابع مشابه
Uniqueness Results for Nonlocal Hamilton-Jacobi Equations
We are interested in nonlocal Eikonal Equations describing the evolution of interfaces moving with a nonlocal, non monotone velocity. For these equations, only the existence of global-in-time weak solutions is available in some particular cases. In this paper, we propose a new approach for proving uniqueness of the solution when the front is expanding. This approach simplifies and extends exist...
متن کاملNonlocal First-order Hamilton-jacobi Equations Modelling Dislocations Dynamics
We study nonlocal first-order equations arising in the theory of dislocations. We prove the existence and uniqueness of the solutions of these equations in the case of positive and negative velocities, under suitable regularity assumptions on the initial data and the velocity. These results are based on new L1-type estimates on the viscosity solutions of first-order HamiltonJacobi Equations app...
متن کاملHamilton-Jacobi-Bellman Equations
This work treats Hamilton-Jacobi-Bellman equations. Their relation to several problems in mathematics is presented and an introduction to viscosity solutions is given. The work of several research articles is reviewed, including the Barles-Souganidis convergence argument and the inaugural papers on mean-field games. Original research on numerical methods for Hamilton-Jacobi-Bellman equations is...
متن کاملA Comparison Principle for Hamilton-jacobi Equations with Discontinuous Hamiltonians
We show a comparison principle for viscosity superand subsolutions to Hamilton-Jacobi equations with discontinuous Hamiltonians. The key point is that the Hamiltonian depends upon u and has a special structure. The supersolution must enjoy some additional regularity.
متن کاملHypercontractivity of Hamilton–jacobi Equations
– Following the equivalence between logarithmic Sobolev inequalities and hypercontractivity showed by L. Gross, we prove that logarithmic Sobolev inequalities are related similarly to hypercontractivity of solutions of Hamilton–Jacobi equations. By the infimum-convolution description of the Hamilton–Jacobi solutions, this approach provides a clear view of the connection between logarithmic Sobo...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Discrete and Continuous Dynamical Systems
سال: 2022
ISSN: ['1553-5231', '1078-0947']
DOI: https://doi.org/10.3934/dcds.2022061