A Phragmén–Lindelöf property of viscosity solutions to a class of doubly nonlinear parabolic equations. Bounded case

Tilak Bhattacharya; Leonardo Marazzi

doi:10.4171/rsmup/37

JournalsrsmupVol. 142pp. 211–259

A Phragmén–Lindelöf property of viscosity solutions to a class of doubly nonlinear parabolic equations. Bounded case

Tilak Bhattacharya
Western Kentucky University, Bowling Green, USA
Leonardo Marazzi
Savannah College of Art and Design, USA

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Abstract

We study Phragmén–Lindelöf properties for viscosity solutions to a class of nonlinear parabolic equations of the type

H (D u, D^{2} u + Z (u) D u \otimes D u) + χ (t) ∣ D u ∣^{σ} - u_{t} = 0

under a certain boundedness condition on $H$ . We also prove similar results for positive solutions to a class of doubly nonlinear equation $H (D u, D^{2} u) - f (u) u_{t} = 0$ .

Cite this article

Tilak Bhattacharya, Leonardo Marazzi, A Phragmén–Lindelöf property of viscosity solutions to a class of doubly nonlinear parabolic equations. Bounded case. Rend. Sem. Mat. Univ. Padova 142 (2019), pp. 211–259

DOI 10.4171/RSMUP/37