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Comparison results for nonlinear degenerate Dirichlet and Neumann problems with general growth in the gradient. (English) Zbl 1211.35125
Summary: This paper deals with both Dirichlet and Neumann problems for a class of nonlinear degenerate elliptic equations with general growth in the gradient. First, we give an existence result of a spherically symmetric solution to the “symmetrized” problems with data depending only on the radials. Second, we prove that the solutions of the original problems can be compared, under a rearrangement, with the solutions of the “symmetrized” problems.

35J70Degenerate elliptic equations
35J60Nonlinear elliptic equations
35J25Second order elliptic equations, boundary value problems
35B06Symmetries, invariants, etc. (PDE)
35B51Comparison principles (PDE)
Full Text: DOI
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