content_image/327703.jpg content_image/327704.jpg content_image/327705.jpg content_image/327707.jpg content_image/327706.jpg
Hence 

Then, applying (4.20), we obtain 

<img src='content_image/327703.jpg'>

<img src='content_image/327704.jpg'>

<img src='content_image/327705.jpg'>

where we used | χ$_{0}$ ( t ) | ≤ 1 and e 2 sϕ ( x,y,t ) ≤ e 2 sϕ ( x,y, 0) for x ∈ D and y ∈ G$_{1}$. 

On the other hand, by substituting t = 0 in (2.1) and applying u ( x, y, 0) = 0 and R ( x, y, 0) ̸ = 0 , for x ∈ D and | y | ≤ 2 L, we get 

By applying (4.22) in (4.21), we have 

<img src='content_image/327707.jpg'>

<img src='content_image/327706.jpg'>

