Fading absorption in non-linear elliptic equations
Annales de l'I.H.P. Analyse non linéaire, Volume 30 (2013) no. 2, pp. 315-336.

We study the equation -Δu+h(x)|u| q-1 u=0, q>1, in + N = N-1 × + where hC( + N ¯), h0. Let (x 1 ,,x N ) be a coordinate system such that + N =[x N >0] and denote a point x N by (x ' ,x N ). Assume that h(x ' ,x N )>0 when x ' 0 but h(x ' ,x N )0 as |x ' |0. For this class of equations we obtain sharp necessary and sufficient conditions in order that singularities on the boundary do not propagate in the interior.

@article{AIHPC_2013__30_2_315_0,
     author = {Marcus, Moshe and Shishkov, Andrey},
     title = {Fading absorption in non-linear elliptic equations},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {315--336},
     publisher = {Elsevier},
     volume = {30},
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     year = {2013},
     doi = {10.1016/j.anihpc.2012.08.002},
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     url = {http://archive.numdam.org/articles/10.1016/j.anihpc.2012.08.002/}
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Marcus, Moshe; Shishkov, Andrey. Fading absorption in non-linear elliptic equations. Annales de l'I.H.P. Analyse non linéaire, Volume 30 (2013) no. 2, pp. 315-336. doi : 10.1016/j.anihpc.2012.08.002. http://archive.numdam.org/articles/10.1016/j.anihpc.2012.08.002/

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