Electron. J. Differential Equations,
Vol. 2019 (2019), No. 118, pp. 112.
An application of global gradient estimates in LorentzMorrey spaces
for the existence of stationary solutions to degenerate diffusive
HamiltonJacobi equations
MinhPhuong Tran, ThanhNhan Nguyen
Abstract:
In mathematics and physics, the KardarParisiZhang equation or
quasilinear stationary version of a timedependent viscous HamiltonJacobi
equation in growing interface and universality classes
is also known as the quasilinear Riccati type equation.
The existence of solutions to this type of equations still remains an
interesting open problem.
In previous studies [36,38], we obtained global bounds and
gradient estimates for quasilinear elliptic equations with measure data.
The main goal of this article is to obtain the existence of a renormalized
solution to the quasilinear stationary solution for the degenerate diffusive
HamiltonJacobi equation with finite measure data in LorentzMorrey spaces.
Submitted May 22, 2019. Published November 11, 2019.
Math Subject Classifications: 35K55, 35K67, 35K65.
Key Words: Degenerate diffusive HamiltonJacobi equation; stationary solution;
quasilinear Riccati type equation; LorentzMorrey space;
uniformly thickness.
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MinhPhuong Tran
Applied Analysis Research Group
Faculty of Mathematics and Statistics
Ton Duc Thang University
Ho Chi Minh city, Vietnam
email: tranminhphuong@tdtu.edu.vn


ThanhNhan Nguyen
Department of Mathematics
Ho Chi Minh City University of Education
Ho Chi Minh city, Vietnam
email: nguyenthnhan@hcmup.edu.vn

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