Electron. J. Diff. Equ.,
Vol. 2015 (2015), No. 288, pp. 124.
Holder continuity of bounded weak solutions to generalized parabolic
pLaplacian equations II: singular case
Sukjung Hwang, Gary M. Lieberman
Abstract:
Here we generalize quasilinear parabolic pLaplacian type equations to
obtain the prototype equation
where g is a nonnegative, increasing, and continuous function trapped
in between two power functions
and
with
.
Through this generalization in the setting
from Orlicz spaces, we provide a uniform proof with a single geometric
setting that a bounded weak solution is locally Holder continuous
with some degree of commonality between degenerate and singular types.
By using geometric characters, our proof does not rely on any of
alternatives which is based on the size of solutions.
Submitted July 17, 2015. Published November 19, 2015.
Math Subject Classifications: 35B45, 35K67.
Key Words: Quasilinear parabolic equation; singular equation;
generalized structure; a priori estimate; Holder continuity.
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Sukjung Hwang
Center for Mathematical Analysis and Computation
Yonsei University, Seoul 03722, Korea
email: sukjung_hwang@yonsei.ac.kr


Gary M. Lieberman
Department of Mathematics
Iowa State University
Ames, IA 50011, USA
email: lieb@iastate.edu

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