Minh-Phuong Tran, Thanh-Nhan Nguyen
Abstract:
In mathematics and physics, the Kardar-Parisi-Zhang equation or
quasilinear stationary version of a time-dependent viscous Hamilton-Jacobi
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
Hamilton-Jacobi equation with finite measure data in Lorentz-Morrey spaces.
Submitted May 22, 2019. Published November 11, 2019.
Math Subject Classifications: 35K55, 35K67, 35K65.
Key Words: Degenerate diffusive Hamilton-Jacobi equation; stationary solution;
quasilinear Riccati type equation; Lorentz-Morrey space;
uniformly thickness.
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Minh-Phuong Tran Applied Analysis Research Group Faculty of Mathematics and Statistics Ton Duc Thang University Ho Chi Minh city, Vietnam email: tranminhphuong@tdtu.edu.vn |
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Thanh-Nhan 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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