Initial-boundary value problem for higher dimensional landau–lifshitz systems

Abstract

This article is concerned with the partial regularity of the weak solutions satisfying energy inequality and monotonicity inequality to the initial-boundary value problem of Landau–Lifshitz system of ferromagnetic spin chain with Gilbert damping in higher dimensions. A generalized monotonicity inequality is derived. The singular set and its Hausdorff dimension are discussed.

Keywords:

• Landau–Lifshitz systems
• Dirichlet problem
• Partial regularity
• 1991 M R Subject Classifications: 35D10
• 35Q80

Acknowledgments

The author is partially supported by the National Natural Science Foundation of China (Grant No. 19971030) and by Guangdong Provincial Natural Science Foundation (Grant No. 000671, No. 031495).

Notes

E-mail: [email protected]

Additional information

Notes on contributors

Boling Guo †

E-mail: [email protected]