论文标题
非线性边界条件的P-Laplacian的自由边界问题
A free boundary problem for the p-Laplacian with nonlinear boundary conditions
论文作者
论文摘要
我们研究了在热绝缘的情况下出现的自由边界问题的非线性概括。 We consider two open sets $Ω\subseteq A$, and we search for an optimal $A$ in order to minimize a non-linear energy functional, whose minimizers $u$ satisfy the following conditions: $Δ_p u=0$ inside $A\setminusΩ$, $u=1$ in $Ω$, and a nonlinear Robin-like boundary $(p,q)$-condition on the free boundary $\partial $。我们研究了SBV中问题的变异表述，并证明，在指数$ p $和$ Q $的适当条件下，存在一个最小化器，其跳转套件可满足均匀密度的估计。
We study a nonlinear generalization of a free boundary problem that arises in the context of thermal insulation. We consider two open sets $Ω\subseteq A$, and we search for an optimal $A$ in order to minimize a non-linear energy functional, whose minimizers $u$ satisfy the following conditions: $Δ_p u=0$ inside $A\setminusΩ$, $u=1$ in $Ω$, and a nonlinear Robin-like boundary $(p,q)$-condition on the free boundary $\partial A$. We study the variational formulation of the problem in SBV, and we prove that, under suitable conditions on the exponents $p$ and $q$, a minimizer exists and its jump set satisfies uniform density estimates.
