Rigidity of the ${{L}^{p}}$-norm of the Poisson bracket on surfaces
Sharpness of the Brascamp–Lieb inequality in Lorentz spaces
June 2017, 24: 38-52. doi: 10.3934/era.2017.24.005
Existence and uniqueness of weak solutions for a class of nonlinear parabolic equations
Peiying Chen
Department of Mathematics, Shanghai University, Shanghai 200444, China
Received December 16, 2016 Revised April 30, 2017 Published June 2017
Fund Project: The author would like to thank her supervisor Prof. Zhongrui Shi, who supported her throughout her paper with his knowledge, patience and excellent guidance
In this paper, we study the Dirichlet boundary value problem of a class of nonlinear parabolic equations. By a priori estimates, difference and variation techniques, we establish the existence and uniqueness of weak solutions of this problem.
Keywords: Existence, uniqueness, weak solution, variation problem, $\mathcal{N}$-function.
Mathematics Subject Classification: 35K55(Primary), 35K61(Secondary), 46B20.
Citation: Peiying Chen. Existence and uniqueness of weak solutions for a class of nonlinear parabolic equations. Electronic Research Announcements, 2017, 24: 38-52. doi: 10.3934/era.2017.24.005
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