Potential theory for elliptic systems
Chen, Z. Q. ; Zhao, Z.
Ann. Probab., Tome 24 (1996) no. 2, p. 293-319 / Harvested from Project Euclid
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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.
Publié le : 1996-01-14
Classification:  Weakly coupled elliptic system,  weak solution,  Dirichlet boundary value problem,  Dirichlet space,  switched diffusion,  irreducibility,  resolvent,  kernel function,  60H30,  35J45,  60J60 
@article{1042644718,
     author = {Chen, Z. Q. and Zhao, Z.},
     title = {Potential theory for elliptic systems},
     journal = {Ann. Probab.},
     volume = {24},
     number = {2},
     year = {1996},
     pages = { 293-319},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1042644718}
}

Chen, Z. Q.; Zhao, Z. Potential theory for elliptic systems. Ann. Probab., Tome 24 (1996) no. 2, pp.  293-319. http://gdmltest.u-ga.fr/item/1042644718/