Tornado solutions for semilinear elliptic equations in ℝ²: regularity

Meadows, Alexander

doi:10.1090/S0002-9939-06-08617-5

Tornado solutions for semilinear elliptic equations in $\mathbb {R}^2$: regularity
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Proc. Amer. Math. Soc. 135 (2007), 1411-1417 Request permission

Abstract:

We give conditions under which bounded solutions to semilinear elliptic equations $\Delta u = f(u)$ on domains of $\mathbb {R}^2$ are continuous despite a possible infinite singularity of $f(u)$. The conditions do not require a minimization or variational stability property for the solutions. The results are used in a second paper to show regularity for a familiar class of equations.

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