MORREY-LORENTZ ESTIMATES for HODGE-TYPE SYSTEMS

Sengupta, B and Sil, S (2025) MORREY-LORENTZ ESTIMATES for HODGE-TYPE SYSTEMS. In: Discrete and Continuous Dynamical Systems- Series A, 45 (1). pp. 334-360.

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Abstract

We prove up to the boundary regularity estimates in Morrey-Lorentz spaces for weak solutions of the linear system of differential forms with regular anisotropic coeficients (Formula-presented) with either v � and v d � (B �) or v �B � and v � (Ad �) prescribed on @: We derive these estimates from the Lp estimates obtained in 32 in the spirit of Campanato's method. Unlike Lorentz spaces, Morrey spaces are neither interpolation spaces nor rearrangement invariant. So, Morrey estimates can not be obtained directly from the Lp estimates using interpolation. We instead adapt an idea of Lieberman 19 to our setting to derive the estimates. Applications to Hodge decomposition in Morrey-Lorentz spaces, Gaffney type inequalities, and estimates for related systems such as Hodge-Maxwell systems and `div-curl' systems are discussed. © 2025 American Institute of Mathematical Sciences. All rights reserved.

Item Type:	Journal Article
Publication:	Discrete and Continuous Dynamical Systems- Series A
Additional Information:	The copyright for this article belongs to the publisher.
Department/Centre:	Division of Physical & Mathematical Sciences > Mathematics
Date Deposited:	19 Sep 2024 09:21
Last Modified:	19 Sep 2024 09:21
URI:	http://eprints.iisc.ac.in/id/eprint/86239

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