Abstract
We report on the solution of two long-standing conjectures on the boundary behavior of maximal solutions of semilinear elliptic equations, focusing on the proof of the boundary regularity of the hyperbolic radius in higher dimensions. The main tool is the reduction of the problem to a degenerate equation of Fuchsian type, for which new Schauder-type estimates are proved. We also sketch an algorithm suitable for large classes of applications.
To Haïm Brezis on the occasion of his sixtieth birthday celebration
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© 2005 Birkhäuser Verlag Basel/Switzerland
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Kichenassamy, S. (2005). Recent Progress on Boundary Blow-up. In: Bandle, C., et al. Elliptic and Parabolic Problems. Progress in Nonlinear Differential Equations and Their Applications, vol 63. Birkhäuser Basel. https://doi.org/10.1007/3-7643-7384-9_33
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DOI: https://doi.org/10.1007/3-7643-7384-9_33
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