Geodesic
Properties of a quasi-uniformly monotone operator and its application to the electromagnetic $p$-$\text {curl}$ systems
Applications of Mathematics, Tome 67 (2022) no. 4, pp. 431-444

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In this paper we propose a new concept of quasi-uniform monotonicity weaker than the uniform monotonicity which has been developed in the study of nonlinear operator equation $Au=b$. We prove that if $A$ is a quasi-uniformly monotone and hemi-continuous operator, then $A^{-1}$ is strictly monotone, bounded and continuous, and thus the Galerkin approximations converge. Also we show an application of a quasi-uniformly monotone and hemi-continuous operator to the proof of the well-posedness and convergence of Galerkin approximations to the solution of steady-state electromagnetic $p$-curl systems.
DOI : 10.21136/AM.2021.0365-20
Classification : 35A15, 35D30, 47H05, 65N30, 78M10, 78M30
Keywords: well-posedness; uniform monotonicity; S-property; $p$-curl systems 
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Song, Chang-Ho; Ri, Yong-Gon; Sin, Cholmin. Properties of a quasi-uniformly monotone operator and its application to the electromagnetic $p$-$\text {curl}$ systems. Applications of Mathematics, Tome 67 (2022) no. 4, pp. 431-444. doi: 10.21136/AM.2021.0365-20

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