We consider a boundary value problem in a bounded domain involving a degenerate operator of the form L(u) = − div a(x)∇u and a suitable nonlinearity f . The function a vanishes on smooth 1-codimensional submanifolds of where it is not allowed to be C2. By using weighted Sobolev spaces we are still able to find existence of solutions which vanish, in the trace sense, on the set where a vanishes.
Multiple solutions for some strongly degenerate second order elliptic equations
Siciliano, Gaetano
2020-01-01
Abstract
We consider a boundary value problem in a bounded domain involving a degenerate operator of the form L(u) = − div a(x)∇u and a suitable nonlinearity f . The function a vanishes on smooth 1-codimensional submanifolds of where it is not allowed to be C2. By using weighted Sobolev spaces we are still able to find existence of solutions which vanish, in the trace sense, on the set where a vanishes.File in questo prodotto:
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