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

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.

### 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
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### References:

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