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

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.

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
Full Text: DOI

References:

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