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Existence and nonexistence of solutions for singular quadratic quasilinear equa...

http://www.sciencedirect.com/science/article/B6WJ2-4VKMWDR-2/2/f35680f147d63f6297e97ebb1b4b242e

A coupled convection-diffusion level set model for tracking epithelial cells in...

Colorectal cancer is initiated in colonic crypts as a consequence of alterations leading to the disruption of the normal colonic cellular process. We propose a new model, which couples a convection-di usion type equation with a level set equation, for tracking the time evolution of an epithelial cell set, inside a colonic crypt, until it reaches the top of the crypt. The convection-di usion equation describes t...

Local estimates for parabolic equations with nonlinear gradient terms

Growth conditions and uniqueness of the Cauchy problem for the evolutionary inf...

We study the Cauchy problem for the parabolic infinity Laplace equation. We prove a new comparison principle and obtain uniqueness of viscosity solutions in the class of functions with a polinomial growth at infinity, improving previous results obtained assuming a linear growth.

Quadratic quasilinear equations with general singularities

Local properties of solutions of elliptic equations depending on local properti...