Fading absorption in non-linear elliptic equations

  • Moshe Marcus

    Department of Mathematics, Technion Haifa, Israel
  • Andrey Shishkov

    Institute of Appl. Math. and Mech., NAS of Ukraine, Donetsk, Ukraine


We study the equation , , in where \( h \in C(\mathbb{R}_{ + }^{N}\limits^{¯}) \), . Let be a coordinate system such that and denote a point by . Assume that when but as . 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.

Cite this article

Moshe Marcus, Andrey Shishkov, Fading absorption in non-linear elliptic equations. Ann. Inst. H. Poincaré Anal. Non Linéaire 30 (2013), no. 2, pp. 315–336

DOI 10.1016/J.ANIHPC.2012.08.002