Geodesic
An inverse boundary-value problem for semilinear elliptic equations
Electronic journal of differential equations, Tome 2010 (2010)
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 
@article{EJDE_2010__2010__a3,
     author = {Sun,  Ziqi},
     title = {An inverse boundary-value problem for semilinear elliptic equations},
     journal = {Electronic journal of differential equations},
     year = {2010},
     volume = {2010},
     zbl = {1189.35380},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2010__2010__a3/}
}
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%J Electronic journal of differential equations
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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__a3/