论文信息 - Potential theory for elliptic systems

Potential theory for elliptic systems

The existence and uniqueness theorem is proved for solutions of the Dirichlet boundary value problems for weakly coupled elliptic systems on bounded domains. The elliptic systems are only assumed to have measurable coefficients and have singular coefficients for the lower-order terms. A probabilistic representation theorem for solutions of the Dirichlet boundary value problems is obtained by using the switched diffusion process associated with the system. A strong positivity result for solutions of the Dirichlet boundary value problems is proved. Formulas expressing resolvents and kernel functions for the system by those of the component elliptic operators are also obtained.

Zhen-Qing Chen | Z. Zhao | Z. Zhao

[1] Tosio Kato. Perturbation theory for linear operators , 1966 .

[2] H. Weinberger,et al. Maximum principles in differential equations , 1967 .

[3] N. Trudinger. Linear elliptic operators with measurable coe cients , 1973 .

[4] Processus de Markov associé a une forme de Dirichlet non symétrique , 1975 .

[5] P. Meyer,et al. Renaissance, recollements, mélanges, ralentissement de processus de Markov , 1975 .

[6] D. Gilbarg,et al. Elliptic Partial Differential Equa-tions of Second Order , 1977 .

[7] M. Fukushima. Dirichlet forms and Markov processes , 1980 .

[8] L. Rogers. GENERAL THEORY OF MARKOV PROCESSES , 1989 .

[9] A. Skorokhod. Asymptotic Methods in the Theory of Stochastic Differential Equations , 2008 .

[10] Mark Freidlin,et al. On the dirichlet problem for a class of second order pde systems with small parameter , 1990 .

[11] Jia-An Yan,et al. Semimartingale Theory and Stochastic Calculus , 1992 .

[12] Y. Kifer. Principal eigenvalues and equilibrium states corresponding to weakly coupled parabolic systems of PDE , 1992 .

[13] Zhen-Qing Chen,et al. Switched diffusion processes and systems of elliptic equations: a Dirichlet space approach , 1994, Proceedings of the Royal Society of Edinburgh: Section A Mathematics.

[14] Zhen-Qing Chen,et al. Diffusion processes and second order elliptic operators with singular coefficients for lower order terms , 1995 .