the space of all linear continuous operators from $X$ to $Y$.

Notation $d$ is always used as the space dimension. In the full text, the Einstein summation convention is adopted, means summing repeated indexes from $1$ to $d$. Without specification, $\Omega$ is a domain (open and bounded set in ${\mathbb{R}}^d$) with Lipschitz boundary $\Gamma$, and denote $\bm{n}$ as the outward unit normal to $\Gamma$. The Sobolev spaces $W^{k,p}$ and $H^{k}$ are defined as usual (see [@Brenner2008]) and we abbreviate the norm and seminorm of Sobolev space $H^k(\Omega)$ as ${\left\lVert  \cdot \right\rVert}_{k,\Omega}$ and ${\left\lvert \cdot \right\rvert}_{k,\Omega}$.

To specify conditions respectively on the different parts of boundary, we rewrite $\Gamma= {    \sbox{\myboxA}{$\m@th\Gamma_D$}    \setbox\myboxB\null    \ht\myboxB=\ht\myboxA    \dp\myboxB=\dp\myboxA    \wd\myboxB=0.75\wd\myboxA    \sbox\myboxB{$\m@th\overline{\copy\myboxB}$}    \setlength\mylenA{\the\wd\myboxA}    \addtolength\mylenA{-\the\wd\myboxB}    \ifdim\wd\myboxB<\wd\myboxA    \rlap{\hskip 0.5\mylenA\usebox\myboxB}{\usebox\myboxA}    \else
    \hskip -0.5\mylenA\rlap{\usebox\myboxA}{\hskip 0.5\mylenA\usebox\myboxB}    \fi} \cup {    \sbox{\myboxA}{$\m@th\Gamma_N$}    \setbox\myboxB\null    \ht\myboxB=\ht\myboxA    \dp\myboxB=\dp\myboxA    \wd\myboxB=0.75\wd\myboxA    \sbox\myboxB{$\m@th\overline{\copy\myboxB}$}    \setlength\mylenA{\the\wd\myboxA}    \addtolength\mylenA{-\the\wd\myboxB}    \ifdim\wd\myboxB<\wd\myboxA    \rlap{\hskip 0.5\mylenA\usebox\myboxB}{\usebox\myboxA}    \else
    \hskip -0.5\mylenA\rlap{\usebox\myboxA}{\hskip 0.5\mylenA\usebox\myboxB}    \fi} \cup {    \sbox{\myboxA}{$\m@th\Gamma_C$}    \setbox\myboxB\null    \ht\myboxB=\ht\myboxA    \dp\myboxB=\dp\myboxA    \wd\myboxB=0.75\wd\myboxA    \sbox\myboxB{$\m@th\overline{\copy\myboxB}$}    \setlength\mylenA{\the\wd\myboxA}    \addtolength\mylenA{-\the\wd\myboxB}    \ifdim\wd\myboxB<\wd\myboxA    \rlap{\hskip 0.5\mylenA\usebox\myboxB}{\usebox\myboxA}    \else
    \hskip -0.5\mylenA\rlap{\usebox\myboxA}{\hskip 0.5\mylenA\usebox\myboxB}    \fi}$, $\Gamma_D$, $\Gamma_N$ and $\Gamma_C$ are open according to the inheriting topology on $\Gamma$ and disjoint with each other, $\Gamma_C \neq \varnothing$ and $\Gamma_D \neq \varnothing$ without specification. We mainly concern functional space $V$ which its functions $u \in H^1(\Omega)$ 