Compact contact sets of sub-quadratic solutions to the thin obstacle problem.(English)Zbl 1537.35425
Summary: We study global solutions to the thin obstacle problem with at most quadratic growth at infinity. We show that every ellipsoid can be realized as the contact set of such a solution. On the other hand, if such a solution has a compact contact set, we show that it must be an ellipsoid.
MSC:
| 35R35 | Free boundary problems for PDEs |
| 35B65 | Smoothness and regularity of solutions to PDEs |
| 35J20 | Variational methods for second-order elliptic equations |
| 35J25 | Boundary value problems for second-order elliptic equations |
| 35J86 | Unilateral problems for linear elliptic equations and variational inequalities with linear elliptic operators |
| 31B20 | Boundary value and inverse problems for harmonic functions in higher dimensions |
Cite
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