JournalsifbVol. 14, No. 2pp. 145–152

Regular solutions to a monodimensional model with discontinuous elliptic operator

  • Piotr B. Mucha

    University of Warsaw, Poland
Regular solutions to a monodimensional model with discontinuous elliptic operator cover
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Abstract

The note examines qualitative behavior of solutions to a monodimensional nonlinear elliptic equation ddx(ux+sgn ux)=f\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.

Cite this article

Piotr B. Mucha, Regular solutions to a monodimensional model with discontinuous elliptic operator. Interfaces Free Bound. 14 (2012), no. 2, pp. 145–152

DOI 10.4171/IFB/276