On evolutionary problems with a-priori bounded gradients
On evolutionary problems with a-priori bounded gradients
Abstract We study a nonlinear evolutionary partial differential equation that can be viewed as a generalization of the heat equation where the temperature gradient is a priori bounded but the heat flux provides merely $$L^1$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mi>L</mml:mi> <mml:mn>1</mml:mn> </mml:msup> </mml:math> -coercivity. Applying higher differentiability techniques in space and …