Global boundedness and Hölder regularity of solutions to general p(x,t)‐Laplace parabolic equations.

In this paper, we establish global boundedness and Hölder regularity of the weak solution to the following parabolic p(x,t)‐Laplace equation: ut−diva(x,t,u,∇u)=b(x,t,u,∇u)inQT,u(x,t)=0on∂Ω×(0,T),u(x,0)=u0inΩ,under some proper assumptions on a and b. The Hölder continuity given in the present work extends known results to the equation with a general nondivergence term. [ABSTRACT FROM AUTHOR]