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Damascelli, Lucio

Comparison theorems for some quasilinear degenerate elliptic operators and applications to symmetry and monotonicity results. (English) Zbl 0911.35009

Ann. Inst. Henri Poincaré, Anal. Non Linéaire 15, No. 4, 493-516 (1998).
Summary: We prove some weak and strong comparison theorems for solutions of differential inequalities involving a class of elliptic operators that includes the \(p\)-Laplacian operator. We then use these theorems together with the method of moving planes and the sliding method to get symmetry and monotonicity properties of solutions to quasilinear elliptic equations in bounded domains.

Cited in 204 Documents

MSC:

35B05 Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs
35J70 Degenerate elliptic equations
35B50 Maximum principles in context of PDEs
35J60 Nonlinear elliptic equations

Keywords:

\(p\)-Laplacian; differential inequalities; moving planes; sliding method
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Full Text: DOI Numdam EuDML

References:

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