Convex configurations for solutions to semilinear elliptic problems in convex rings

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Issue Date
2006-05
Authors
Acker, Andrew
Poghosyan, Mikayel
Shahgholian, Henrik
Advisor
Citation

Acker, A., M. Poghosyan, et al. (2006). "Convex Configurations for Solutions to Semilinear Elliptic Problems in Convex Rings." Communications in Partial Differential Equations 31(9): 1273-1287.

Abstract

For a given convex ring and an L 1 function f:Ω × → + we show, under suitable assumptions on f, that there exists a solution (in the weak sense) to

with {x Ω: u(x) > s} Ω1 convex, for all s (0, M).

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