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Serrin, James; Zou, Henghui

Cauchy-Liouville and universal boundedness theorems for quasilinear elliptic equations and inequalities. (English) Zbl 1059.35040

Acta Math. 189, No. 1, 79-142 (2002).
The paper has essentially two main goals. The first one is to prove Liouville type results for degenerate problems of the type \[ \Delta_mu + f(u) = 0, \;\;u\geq 0 \] in a connected open set, considering also in particular the case \[ f(u) = u^{p-1},\;p>1. \] The second one is to derive universal estimates for the solutions of the previous problem, where universal means in particular independent from boundary conditions.
Reviewer: Marco Biroli (Milano)

Cited in 1 Review
Cited in 212 Documents

MSC:

35J60 Nonlinear elliptic equations
35B05 Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs
35B45 A priori estimates in context of PDEs

Keywords:

nonlinear elliptic equations; Liouville type properties; a priori estimates
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