In this paper we prove a general result giving the maximum and the antimaximum principles in a unitary way for linear operators of the form $L+\lambda I$, provided that 0 is an eigenvalue of L with associated constant eigenfunctions. To this purpose, we introduce a new notion of "quasi"-uniform maximum principle, named k-uniform maximum principle: it holds for lambda belonging to certain neighborhoods of 0 depending on the fixed positive multiplier k > 0 which selects the good class of right-hand-sides. Our approach is based on a $L^infinity$ - $L^p$ estimate for some related problems. As an application, we prove some generalization and new results for elliptic problems and for time periodic parabolic problems under Neumann boundary conditions

Quasi uniformity for the abstract Neumann antimaximum principle and applications with a priori estimates

FRAGNELLI, Genni;
2013-01-01

Abstract

In this paper we prove a general result giving the maximum and the antimaximum principles in a unitary way for linear operators of the form $L+\lambda I$, provided that 0 is an eigenvalue of L with associated constant eigenfunctions. To this purpose, we introduce a new notion of "quasi"-uniform maximum principle, named k-uniform maximum principle: it holds for lambda belonging to certain neighborhoods of 0 depending on the fixed positive multiplier k > 0 which selects the good class of right-hand-sides. Our approach is based on a $L^infinity$ - $L^p$ estimate for some related problems. As an application, we prove some generalization and new results for elliptic problems and for time periodic parabolic problems under Neumann boundary conditions
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11586/63107
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