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math.AP2013
Qualitative Analysis of Rupture Solutions for an MEMS Problem
Juan Davila, Kelei Wang, Juncheng Wei
We prove a sharp Hölder continuity estimates of rupture sets for sequences of solutions of the following nonlinear problem with negative exponent $$ Δu= \frac{1}{u^p}, \ p>1, \ \mb…
math.AP2013★ 2 cited
A Monotonicity Formula and a Liouville-type Theorem for a Fourth Order Supercritical Problem
Juan Davila, Louis Dupaigne, Kelei Wang +1
We consider Liouville-type and partial regularity results for the nonlinear fourth-order problem $$ Δ^2 u=|u|^{p-1}u\ \{in} \ \R^n,$$ where and . We give a complete c…