An existence result for nonhomogeneous quasilinear parabolic equations\n beyond the duality pairing

2019/01/07 by Karthik Adimurthi, Adimurthi, Karthik, Sun‐Sig Byun +3
Mathematics · Engineering · #Nonlinear Partial Differential Equations #Advanced Mathematical Physics Problems #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.1901.01998

Abstract

In this paper, we prove existence of \very weak solutions to\nnonhomogeneous quasilinear parabolic equations beyond the duality pairing. The\nmain ingredients are a priori esitmates in suitable weighted spaces combined\nwith the compactness argument developed in citebulicek2018well. In order to\nobtain the a priori estimates, we make use of the full Calder 'on-Zygmund\nmachinery developed in the past few years and combine it with some sharp bounds\nfor the subclass of Muckenhoupt weights considered in this paper.\n

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