## Regularity of viscosity solutions of a degenerate parabolic equation

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- by Yun-Guang Lu and Liwen Qian
- Proc. Amer. Math. Soc.
**130**(2002), 999-1004 - DOI: https://doi.org/10.1090/S0002-9939-01-06313-4
- Published electronically: November 9, 2001
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## Abstract:

We study the Cauchy problem for the nonlinear degenerate parabolic equation of second order \[ \left \{ \begin {array}{l} u_t=u\triangle u-\gamma |\nabla u|^2 \ \ \text {in} \hspace {0.3cm} \Omega =R^N \times R^{+}, u(x,0)=u_{0}(x)\ \ \ \ \ \ \ \ \text {in} \hspace {0.3cm} R^{N}, \end {array} \right . \] and present regularity results for the viscosity solutions.## References

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## Bibliographic Information

**Yun-Guang Lu**- Affiliation: Departamento de Matematicas y Estadistica, Universidad Nacional de Colombia, Bogota, Colombia
- Email: yglu@matematicas.unal.edu.co
**Liwen Qian**- Affiliation: Department of Computational Science, National University of Singapore, Singapore 117543
- Address at time of publication: Singapore-MIT Alliance, National University of Singapore, Singapore 119260
- Email: qianlw@cz3.nus.edu.sg, smaqlw@nus.edu.sg
- Received by editor(s): November 1, 1998
- Received by editor(s) in revised form: April 10, 2000
- Published electronically: November 9, 2001
- Communicated by: Suncica Canic
- © Copyright 2001 American Mathematical Society
- Journal: Proc. Amer. Math. Soc.
**130**(2002), 999-1004 - MSC (2000): Primary 35K55; Secondary 35K65, 35D10
- DOI: https://doi.org/10.1090/S0002-9939-01-06313-4
- MathSciNet review: 1873772