Geodesic
Regular solutions to a monodimensional model with discontinuous elliptic operator
Piotr Bogusław Mucha1
1University of Warsaw, Poland
Interfaces and free boundaries, Tome 14 (2012) no. 2, pp. 145-152

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DOI

The note examines qualitative behavior of solutions to a monodimensional nonlinear elliptic equation dxd​(ux​+sgn ux​)=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.
DOI : 10.4171/ifb/276
Classification : 35-XX, 74-XX, 94-XX, 00-XX
Mots-clés : Singular elliptic operator, discontinuity, facets, qualitative analysis, structure of solutions

Piotr Bogusław Mucha  1

1 University of Warsaw, Poland 
Piotr Bogusław Mucha. Regular solutions to a monodimensional model with discontinuous elliptic operator. Interfaces and free boundaries, Tome 14 (2012) no. 2, pp. 145-152. doi: 10.4171/ifb/276
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     number = {2},
     doi = {10.4171/ifb/276},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/ifb/276/}
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