"note environment" with mdframed

Question

Here is what I have: And here is what I would like:

---

The code to get what I currently have:

\documentclass[a4paper, 11pt]{article}

\usepackage[english]{babel}
\usepackage[utf8]{inputenc}
\usepackage[T1]{fontenc}
\usepackage{lmodern}
\usepackage{xcolor}
\usepackage[framemethod=default]{mdframed}

\global\mdfdefinestyle{exampledefault}{%
linecolor=lightgray,linewidth=1pt,%
leftmargin=1cm,rightmargin=1cm
}

\begin{document}

\begin{mdframed}[style=exampledefault, frametitle={Note}]
This is my note.
\end{mdframed}

\end{document}

Answer 1

You could proceed as follows:

\documentclass{article}
\usepackage{xcolor}
\usepackage[framemethod=default]{mdframed}

\global\mdfdefinestyle{exampledefault}{%
linecolor=lightgray,linewidth=1pt,%
leftmargin=1cm,rightmargin=1cm,
}

\newenvironment{mymdframed}[1]{%
\mdfsetup{%
frametitle={\colorbox{white}{\,#1\,}},
frametitleaboveskip=-\ht\strutbox,
frametitlealignment=\raggedright
}%
\begin{mdframed}[style=exampledefault]
}{\end{mdframed}}


\begin{document}

\begin{mymdframed}{Note}
This is my note.
\end{mymdframed}
\end{document}

The result:

This method provides some space between and after the title. If you don't want them:

\documentclass{article}
\usepackage{tikz}
\usepackage[framemethod=default]{mdframed}

\global\mdfdefinestyle{exampledefault}{%
linecolor=lightgray,linewidth=1pt,%
leftmargin=1cm,rightmargin=1cm,
}

\newenvironment{mymdframed}[1]{%
\mdfsetup{%
frametitle={\tikz\node[fill=white,rectangle,inner sep=0pt,outer sep=0pt]{#1};},
frametitleaboveskip=-0.5\ht\strutbox,
frametitlealignment=\raggedright
}%
\begin{mdframed}[style=exampledefault]
}{\end{mdframed}}


\begin{document}

\begin{mymdframed}{Note}
This is my note.
\end{mymdframed}
\end{document}

The result: