Abstract
We establish local continuity of locally bounded weak solutions to a doubly nonlinear parabolic equation that models the temperature in multi-phase transitions. The enthalpy allows for general maximal monotone graphs of the temperature. Remarkably, moduli of continuity can be estimated without an explicit form of the enthalpy.
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Acknowledgement
U. Gianazza was supported by the grant 2017TEXA3H 002 “Gradient flows,Optimal Transport and MetricMeasure Structures”. N. Liao was supported by the FWF–Project P31956–N32 “Doubly nonlinear evolution equations”. We thank the referee for careful reading and comments.
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Gianazza, U., Liao, N. Continuity of the Temperature in a Multi-Phase Transition Problem. Part III. JAMA 150, 583–607 (2023). https://doi.org/10.1007/s11854-023-0283-2
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DOI: https://doi.org/10.1007/s11854-023-0283-2