Symmetry in a parabolic multi-phase overdetermined problem. (English) Zbl 1277.35265
This paper is concerned with the problem of symmetry of domains related to parabolic overdetermined problems. Given a non-constant function satisfying
\[
(\Delta-\partial_t)u=-\delta_0 \text{ in }\Omega\quad{\text{and} } \quad u=0 \text{ on } \partial_{\text{par}}\Omega,
\]
the author presents some conditions that \(\partial_{n_x}u\) satisfies on \( \partial_{\text{par}}\Omega\setminus \{t=0\}\), which guarantees the domain \(\Omega\) is, in fact, a heat ball.
Reviewer: Sérgio Luís Zani (São Carlos)
MSC:
35N05 | Overdetermined systems of PDEs with constant coefficients |
35B06 | Symmetries, invariants, etc. in context of PDEs |
35R35 | Free boundary problems for PDEs |
35K20 | Initial-boundary value problems for second-order parabolic equations |
35K08 | Heat kernel |
Keywords:
symmetry of domainsReferences:
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