Description: |
This work consists of two parts: In the first part we study nonnegative minimizers of degenerate elliptic functionals for variational kernels that are discontinuous. The Euler-Lagrange equation is therefore governed by a non-homogeneous, degenerate elliptic equation with free boundary between the positive and the zero phases of the minimizer. We show optimal gradient estimate and nondegeneracy of minima. We also address weak and strong regularity properties of free boundary. In the second part of work we provide a rather complete description of the sharp regularity theory for a family of heterogeneous, two-phase variational free boundary problems, ruled by nonlinear, degenerate elliptic operators.
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