Geodesic
An inverse boundary-value problem for semilinear elliptic equations
Electronic Journal of Differential Equations, Tome 2010 (2010).

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

Summary: We show that in dimension two or greater, a certain equivalence class of the scalar coefficient $a(x,u)$ of the semilinear elliptic equation $\Delta u\,+a(x,u)=0$ is uniquely determined by the Dirichlet to Neumann map of the equation on a bounded domain with smooth boundary. We also show that the coefficient $a(x,u)$ can be determined by the Dirichlet to Neumann map under some additional hypotheses.
Classification : 35R30
Keywords: inverse problem, Dirichlet to Neumann map 
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     author = {Sun, Ziqi},
     title = {An inverse boundary-value problem for semilinear elliptic equations},
     journal = {Electronic Journal of Differential Equations},
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     volume = {2010},
     year = {2010},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2010__2010__a203/}
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Sun, Ziqi. An inverse boundary-value problem for semilinear elliptic equations. Electronic Journal of Differential Equations, Tome 2010 (2010). http://geodesic.mathdoc.fr/item/EJDE_2010__2010__a203/