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Isoperimetric inequalities in quasilinear elliptic equations of Leray-Lions type. (English) Zbl 0859.35028
A kind of quasilinear elliptic partial differential equation of Leray-Lions type is considered. As the base, the author introduces and proves a pointwise comparison principle for some nonlinear ordinary differential equations. Moreover, the existence and the uniqueness of spherically symmetric solution for the suitable symmetrized partial differential equation is shown. Then by the preceding results, the author gives symmetrization results, precise a priori estimates and the existence of a solution for the main equation. Finally, an application of the preceding results to a general asymptotic problem associated with Leray-Lions operators is announced.

35J60Nonlinear elliptic equations
26D10Inequalities involving derivatives, differential and integral operators
35B05Oscillation, zeros of solutions, mean value theorems, etc. (PDE)
34C11Qualitative theory of solutions of ODE: growth, boundedness