Undefined index: name in:

Estou com um problema, ao manter o valor no input, depois que o usuário da refresh na página. Alguém poderia me ajudar?

O código é esse:

<?php 

      if(isset($_SESSION['name']) || isset($_SESSION['lastname']) || isset($_SESSION['username']) || isset($_SESSION['email']) || isset($_SESSION['emailconf']) || isset($_SESSION['password'])) {
      $_SESSION['name'];
      $_SESSION['lastname'];
      $_SESSION['username'];
      $_SESSION['email'];
      $_SESSION['emailconf'];
      $_SESSION['password'];
    }
    if (isset($_POST['submit'])) {

      $message = null;

      if(isset($_POST['name'])) {
        if(empty($_POST['name'])) {
          $name = clearstring($_POST['name']);
            $message = '<div class="alert alert-warning alert-dismissible fade in" role="alert">
              <button type="button" class="close" data-dismiss="alert" aria-label="Close">
                <span aria-hidden="true">×</span>
                <span class="sr-only">Close</span>
              </button>
              <i class="fa fa-info-circle"></i> Coloque seu nome.
            </div>';
          } else if(isset($_POST['lastname'])) {
        if(empty($_POST['lastname'])) {
          $lastname = clearstring($_POST['lastname']);
            $message = '<div class="alert alert-warning alert-dismissible fade in" role="alert">
              <button type="button" class="close" data-dismiss="alert" aria-label="Close">
                <span aria-hidden="true">×</span>
                <span class="sr-only">Close</span>
              </button>
              <i class="fa fa-info-circle"></i> Coloque seu sobrenome.
            </div>';
        } else if(isset($_POST['username'])) {
        if(empty($_POST['username'])) {
          $username = clearstring($_POST['username']);
            $message = '<div class="alert alert-warning alert-dismissible fade in" role="alert">
              <button type="button" class="close" data-dismiss="alert" aria-label="Close">
                <span aria-hidden="true">×</span>
                <span class="sr-only">Close</span>
              </button>
              <i class="fa fa-info-circle"></i> Coloque um nome de usuário.
            </div>';
        } else if(isset($_POST['email'])) {
        if(empty($_POST['email'])) {
          $email = clearstring($_POST['email']);
            $message = '<div class="alert alert-warning alert-dismissible fade in" role="alert">
              <button type="button" class="close" data-dismiss="alert" aria-label="Close">
                <span aria-hidden="true">×</span>
                <span class="sr-only">Close</span>
              </button>
              <i class="fa fa-info-circle"></i> Coloque seu e-mail.
            </div>';
        } else if(isset($_POST['emailconf'])) {
        if(empty($_POST['emailconf'])) {
          $emailconf = clearstring($_POST['emailconf']);
            $message = '<div class="alert alert-warning alert-dismissible fade in" role="alert">
              <button type="button" class="close" data-dismiss="alert" aria-label="Close">
                <span aria-hidden="true">×</span>
                <span class="sr-only">Close</span>
              </button>
              <i class="fa fa-info-circle"></i> Confirme seu e-mail.
            </div>';
        } else if(isset($_POST['password'])) {
        if(empty($_POST['password'])) {
          $password = clearstring($_POST['password']);
            $message = '<div class="alert alert-warning alert-dismissible fade in" role="alert">
              <button type="button" class="close" data-dismiss="alert" aria-label="Close">
                <span aria-hidden="true">×</span>
                <span class="sr-only">Close</span>
              </button>
              <i class="fa fa-info-circle"></i> Coloque uma senha.
            </div>';
        } 
        } 
        } 
        } 
      }
    }
  }


      echo $message;
    }

     ?>
      <form name="assignup" id="assignup" action="" method="post">
        <fieldset class="form-group">
        <div class="row">
          <div class="col-xs-6">
            <input type="text" class="form-control form-control-md" name="name" id="name" value="<?php echo $_POST['name']; ?>" placeholder="Nome">
          </div>
          <div class="col-xs-6">
            <input type="text" class="form-control form-control-md" name="lastname" id="lastname" placeholder="Sobrenome">
          </div>
        </div>
        </fieldset>
        <fieldset class="form-group">
          <input type="text" class="form-control form-control-md" name="username" id="username" placeholder="Usuário">
        </fieldset>
        <fieldset class="form-group">
          <input type="text" class="form-control form-control-md" name="email" id="email" placeholder="E-mail">
        </fieldset>
         <fieldset class="form-group">
          <input type="text" class="form-control form-control-md" name="emailconf" id="emailconf" placeholder="Confirme Seu E-mail">
        </fieldset>
         <fieldset class="form-group">
         <div class="row">
          <div class="col-xs-12 col-md-8">
          <input type="password" class="form-control form-control-md" name="password" id="password" placeholder="Nova Senha">
          </div>
          <div class="col-xs-6 col-md-4">
            <button type="submit" name="submit" class="btn btn-primary">Cadastrar</button>
          </div>
        </fieldset>
        <small class="text-muted">Ao clicar em cadastrar, você concorda com nossos <a href="#">termos de uso</a> que leu nossa <a href="#">politica de dados</a>. Isso inclui o <a href="#">uso de cookies</a>.</small>
        <br>
      </form>