Non funziona. Ti mando il codice vedi se ti funziona.
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN" "http://www.w3.org/TR/html4/loose.dtd">
<html>
<head>
<meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1">
<title>Untitled Document</title>
</head>

<body>

<?php
$test="luca";
?>

<form action="validazione_form1.php" method="post">
Nome : <input type="text" name="nome" >

Cognome : <input type="text" name="cognome" value="<?php $test ?>">

<input type="submit" name="submit" value="invia">
</form>


</body>
</html>