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On a nonlocal elliptic problem. (English) Zbl 0995.35023

Summary: We study stationary solutions of the system \[ u_t =\nabla \cdot \bigg({m-1 \over m} \nabla u^m + u \nabla \varphi \bigg), \quad \;m>1,\quad\;{\varDelta} \varphi = \pm u, \] defined in a bounded domain \({\varOmega}\) of \({\mathbb R}^n\). The physical interpretation of the above system comes from the porous medium theory and semiconductor physics.

MSC:

35J70 Degenerate elliptic equations
35Q72 Other PDE from mechanics (MSC2000)
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