Geodesic
Asymptotic representation of solutions to the Dirichlet problem for elliptic systems with discontinuous coefficients near the boundary
Electronic Journal of Differential Equations, Tome 2006 (2006).

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: We consider variational solutions to the Dirichlet problem for elliptic systems of arbitrary order. It is assumed that the coefficients of the principal part of the system have small, in an integral sense, local oscillations near a boundary point and other coefficients may have singularities at this point. We obtain an asymptotic representation for these solutions and derive sharp estimates for them which explicitly contain information on the coefficients.
Classification : 35B40, 35B65, 35J15, 35D10
Keywords: asymptotic behaviour of solutions, elliptic systems, Dirichlet problem, measurable coefficients 
@article{EJDE_2006__2006__a167,
     author = {Kozlov, Vladimir},
     title = {Asymptotic representation of solutions to the {Dirichlet} problem for elliptic systems with discontinuous coefficients near the boundary},
     journal = {Electronic Journal of Differential Equations},
     publisher = {mathdoc},
     volume = {2006},
     year = {2006},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2006__2006__a167/}
}
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Kozlov, Vladimir. Asymptotic representation of solutions to the Dirichlet problem for elliptic systems with discontinuous coefficients near the boundary. Electronic Journal of Differential Equations, Tome 2006 (2006). http://geodesic.mathdoc.fr/item/EJDE_2006__2006__a167/