$$\Omega \subset \Bbb{R}^m$$ $$\sum_{i,j=1}^m \frac{\partial}{\partial x_i}(a_{ij}(\bar x)\frac{\partial u}{\partial x_j}) + a_0(\bar x)u = f(\bar x)$$
$$a_{ij}\in C^1(\bar \Omega),\ a_0\in C(\bar\Omega),\ a_{ij}(\bar x) = a_{ji}(\bar x)$$
$$\frac{\partial u}{\partial n} = \sum_{i,j=1}^m a_{ij}\frac{\partial u}{\partial x_i}cos(\bar n,\bar x^j) $$
there is $\lambda_0$ such that for any real numbers $\xi_1,...,\xi_n$ and for any $\bar x \in \Omega$ $$\sum_{i,j=1}^m a_{ij}(\bar x)\xi_i\xi_j \ge \lambda_0\sum_{i=1}^m\xi_i^2$$
$$\sigma\in C(\Gamma),\ \sigma(\bar x) \ge 0,\ \bar x\in \Gamma$$
Domain of an operator of elliptic equation with Robin boundary condition: $$ D = \{u\in C^2(\bar\Omega)\ |\ (\frac{\partial u}{\partial n} + \sigma u)(\bar x) = 0, \bar x \in \Gamma\ \text{almost\ everywhere}\} $$ $$ How\ to\ prove\ that\ D_A\ is\ dense\ in\ H^1(\Omega) ? $$
