I need to find a function $L(\phi)$ such that the functional $G=\int_{\Gamma} L(\phi) ds $ has a variation $$\frac{e^{\phi(s)}}{\int_{\Gamma} e^{\phi(t)} dt },$$ where $\Gamma$ is a 3D surface. In other words $L(\phi)$ shall be such that $$\frac{d L(\phi)}{d \phi} = \frac{e^{\phi(s)}}{\int_{\Gamma} e^{\phi(t)} dt },$$ and I was stucked here. What will $L(\phi)$ be? Thanks.
