Continuity Properties of Solutions to Some Degenerate Elliptic Equations
نویسندگان
چکیده
We consider a nonlinear (possibly) degenerate elliptic operator Lv = − div a(∇v) + b(x, v) where the functions a and b are, unnecessarly strictly, monotonic. For a given boundary datum φ we prove the existence of the maximum and the minimum of the solutions and formulate a Haar-Rado type result, namely a continuity property for these solutions that may follow from the continuity of φ. In the homogeneous case we formulate a generalization of the Bounded Slope Condition and use it to obtain the existence of solutions to Lv = 0 that are Lipschitz, or locally Lipschitz, or Hölder upon the behavior of φ.
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