Existence and uniqueness of solutions to parabolic equations with superlinear Hamiltonians
A Davini - Communications in Contemporary Mathematics, 2019 - World Scientific
Communications in Contemporary Mathematics, 2019•World Scientific
We give a proof of existence and uniqueness of viscosity solutions to parabolic quasilinear
equations for a fairly general class of nonconvex Hamiltonians with superlinear growth in the
gradient variable. The approach is mainly based on classical techniques for uniformly
parabolic quasilinear equations and on the Lipschitz estimates provided in [SN Armstrong
and HV Tran, Viscosity solutions of general viscous Hamilton–Jacobi equations, Math. Ann.
361 (2015) 647–687], as well as on viscosity solution arguments.
equations for a fairly general class of nonconvex Hamiltonians with superlinear growth in the
gradient variable. The approach is mainly based on classical techniques for uniformly
parabolic quasilinear equations and on the Lipschitz estimates provided in [SN Armstrong
and HV Tran, Viscosity solutions of general viscous Hamilton–Jacobi equations, Math. Ann.
361 (2015) 647–687], as well as on viscosity solution arguments.
We give a proof of existence and uniqueness of viscosity solutions to parabolic quasilinear equations for a fairly general class of nonconvex Hamiltonians with superlinear growth in the gradient variable. The approach is mainly based on classical techniques for uniformly parabolic quasilinear equations and on the Lipschitz estimates provided in [S. N. Armstrong and H. V. Tran, Viscosity solutions of general viscous Hamilton–Jacobi equations, Math. Ann. 361 (2015) 647–687], as well as on viscosity solution arguments.
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