Oblique Derivative Problem for Parabolic Systems with Quadratic Nonlinearity in Gradient. Boundary Regularity Results
摘要
We consider a class of quasilinear parabolic systems with strong (quadratic) nonlinearity in the gradient. Under a one-sided condition on the quadratic term, we study the boundary regularity of weak solutions to the oblique derivative problem. We describe conditions that guarantee the local Hölder continuity of weak (possibly unbounded) solutions.