Regular solutions to a monodimensional model with discontinuous elliptic operator
Piotr B. Mucha · Interfaces and Free Boundaries Mathematical Analysis Computation and Applications · 2012
The note examines qualitative behavior of solutions to a monodimensional nonlinear elliptic equation \frac{d}{dx}(u_x+\mathrm {sgn} \ u_x)=f with Dirichlet boundary data. This simple example explains the phenomenon of facets – flat regions of solutions, characteristic for models arising from theories of crystal growth and image prossessing.