A priori bounds for degenerate and singular evolutionary partial integro-differential equations

作者：Vergara Vicente; Zacher Rico^*

来源：Nonlinear Analysis-Theory Methods & Applications, 2010, 73(11): 3572-3585.

DOI：10.1016/j.na.2010.07.039

• Integro-differential equation
• Quasilinear equation
• p-Laplacian
• Fractional derivative
• Degenerate parabolic equation
• Weak solution
• Energy estimates
• De Giorgi technique

We study quasilinear evolutionary partial integro-differential equations of second order which include time fractional p-Laplace equations of time order less than one. By means of suitable energy estimates and De Giorgi's iteration technique we establish results asserting the global boundedness of appropriately defined weak solutions of these problems. We also show that a maximum principle is valid for such equations.

• 出版日期2010-12-1