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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:
35B05Oscillation, zeros of solutions, mean value theorems, etc. (PDE)
35J70Degenerate elliptic equations
35B50Maximum principles (PDE)
35J60Nonlinear elliptic equations