How to draw rounded corners around box with shadow

Another idea considering the mdframed package rev. 212 with the use of TikZ. If you want to increase the rounded corner you increase the value 8pt. And for the thickness of the border you increase the value of middlelinewidth=2pt.

documentclass[a4paper,12pt]{article}
usepackage[framemethod=tikz]{mdframed}
usetikzlibrary{shadows}
newmdenv[tikzsetting={draw=gray,fill=white},
          roundcorner=8pt,shadow=true]{mdboxshad}
mdfsetup{%
middlelinewidth=2pt
}
begin{document}

begin{mdboxshad}
The content of this chapter has been published in the SRRW conference in 2017.  The work of this chapter is also extended to handle the ER problem. 
end{mdboxshad}

end{document}

Another alternative without the use of mdframed can be with pure TikZ using the library shadows to make the drop shadows at the below-right:

documentclass[a4paper, 12pt]{article} 
usepackage[utf8]{inputenc} 
usepackage{tikz} 
usetikzlibrary{shadows}

newcommand{mybox}[2]{
    begin{figure}[h]
        centering
    begin{tikzpicture}
        node[anchor=text, text width=textwidth, draw=gray, rounded corners, line width=1.5pt, drop shadow={shadow xshift=.7ex, shadow yshift=-.7ex},fill=#1, inner sep=3mm] (big) {\#2};
            end{tikzpicture}
    end{figure}
}
begin{document}
mybox{white}{The content of this chapter has been published in the SRRW conference in 2017. The work of this chapter is also extended to handle the ER problem.}
end{document}

documentclass{article}
usepackage{tcolorbox}
tcbuselibrary{skins}
begin{document}

begin{tcolorbox}[enhanced jigsaw,drop shadow=black!50!white,colback=white]
The content of this chapter has been published in the SRRW conference in 2017.  The work of this chapter is also extended to handle the ER problem. 
end{tcolorbox}
end{document}

If you want to use the same style of box multiple times in your document, you can also define it in the preamble using newtcolorbox:

documentclass{article}
usepackage{tcolorbox}
tcbuselibrary{skins}

newtcolorbox{mybox}
{
  enhanced jigsaw,
  drop shadow=black!50!white,
  colback=white
}

begin{document}

begin{mybox}
The content of this chapter has been published in the SRRW conference in 2017.  The work of this chapter is also extended to handle the ER problem. 
end{mybox}
end{document}