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Zbl 0911.35009
Damascelli, Lucio
Comparison theorems for some quasilinear degenerate elliptic operators and applications to symmetry and monotonicity results. (English)
[J] Ann. Inst. Henri Poincaré, Anal. Non Linéaire 15, No.4, 493-516 (1998). ISSN 0294-1449

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 2000:: *35B05 General behavior of solutions of PDE
35J70 Elliptic equations of degenerate type
35B50 Maximum principles (PDE)
35J60 Nonlinear elliptic equations

Keywords: $p$-Laplacian; differential inequalities; moving planes; sliding method

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