Improvements on overdetermined problems associated to the $ p $-Laplacian
2022
This work presents some improvements on related papers that investigate certain overdetermined problems associated to elliptic quasilinear operators. Our model operator is the $ p $-Laplacian. Under suitable structural conditions, and assuming that a solution exists, we show that the domain of the problem is a ball centered at the origin. Furthermore we discuss a convenient form of comparison principle for this kind of problems.
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