Critical points of solutions to a kind of linear elliptic equations in multiply connected domains
نویسندگان
چکیده
In this paper, we mainly study the critical points and zero of solutions u to a kind linear elliptic equations with nonhomogeneous Dirichlet boundary conditions in multiply connected domain Ω ℝ2. Based on delicate analysis about distributions components super-level sets {x ∈ Ω: u(x) > t} sub-level < for some t, obtain geometric structure interior point u. Precisely, let be γI external γE, where u∣γI = ψ1(x), u∣γE ψ2(x). When ψ1(x) ψ2(x) have N1 N2 local maximal γE respectively, deduce that $$\sum\nolimits_{i 1}^k {{m_i} \le {N_1} + {N_2}} $$ , m1,…,mk are respective multiplicities x1,…,xk addition, when $${\min _{{\gamma _E}}}{\psi _2}\left( x \right) \ge {\max _I}}}{\psi _1}\left( \right)$$ has only equal maxima relative $$\overline \Omega γe develop new method show one following three results holds or 1 2 . Moreover, investigate We sum is less than half number its isolated boundaries.
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ژورنال
عنوان ژورنال: Israel Journal of Mathematics
سال: 2022
ISSN: ['1565-8511', '0021-2172']
DOI: https://doi.org/10.1007/s11856-022-2330-6