An application of global gradient estimates in Lorentz-Morrey spaces for the existence of stationary solutions to degenerate diffusive Hamilton-Jacobi equations
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 equ...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Texas State University
2019-11-01
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| Series: | Electronic Journal of Differential Equations |
| Subjects: | |
| Online Access: | http://ejde.math.txstate.edu/Volumes/2019/118/abstr.html |
| Summary: | 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. |
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| ISSN: | 1072-6691 |