An application of global gradient estimates in Lorentz-Morrey spaces for the existence of stationary solutions to degenerate diffusive Hamilton-Jacobi equations
Files
Date
2019-11-11
Authors
Tran, Minh-Phuong
Nguyen, Thanh-Nhan
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University, Department of Mathematics
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.
Description
Keywords
Degenerate diffusive Hamilton-Jacobi equation, Stationary solution, Quasilinear Riccati type equation, Lorentz-Morrey space, Uniformly thickness
Citation
Tran, M. P., & Nguyen, T. N. (2019). An application of global gradient estimates in Lorentz-Morrey spaces for the existence of stationary solutions to degenerate diffusive Hamilton-Jacobi equations. <i>Electronic Journal of Differential Equations, 2019</i>(118), pp. 1-12.
Rights
Attribution 4.0 International