Hausdorff Dimension of Ruptures for Solutions of a Semilinear Elliptic Equation with Singular Nonlinearity

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Mathematical Analysis of Partial Differential Equations Modeling Electrostatic MEMS (2010, background): “Related work can also be found in [93, 94, 101, 107, 115, 129, 147].”
Infinitely many turning points for an elliptic problem with a singular non‐linearity (2008, background): “A monotonicity inequality In this section we will obtain a monotonicity inequality similar to that in [15] for non-negative finite energy stationary solutions u ∈ H(1)(Ω) and |x|αu−p ∈ L(1)loc(Ω) of the equation Δu = λ|x|αu−p in Ω, (2.”
Properties of positive solutions of an Elliptic Equation with negative exponents (2007, background): “we can get a non-negative minimizer of J(� ) on A. For such a minimizer, one need to handle with how large for its zero set. One may see [24] and [ 14 ] for more.”