Nginx proxy_pass and absolute paths

I'm trying to run some nodejs app on a server (Ubuntu 14.04), using Nginx and i'm almost done. Here's my server configuration (/etc/nginx/sites-available/default):

server {
    listen 80;
    server_name my_domain.com;

    location /test1 {
        proxy_pass http://127.0.0.1:5000/;
        proxy_http_version 1.1;
        proxy_set_header Upgrade $http_upgrade;
        proxy_set_header Connection 'upgrade';
        proxy_set_header Host $host;
        proxy_cache_bypass $http_upgrade;
    }

    location /test2 {
        proxy_pass http://127.0.0.1:5001/;
        proxy_http_version 1.1;
        proxy_set_header Upgrade $http_upgrade;
        proxy_set_header Connection 'upgrade';
        proxy_set_header Host $host;
        proxy_cache_bypass $http_upgrade;
    }
}

I've got several apps running, and they all works well, i can acces them with http://my_domain.com/test1, http://my_domain.com/test2, etc...

The problem is that inside one of this apps i've got several absolute paths:
e.g. <a href="/">Home</a>
or (inside express)
res.redirect('/');

This redirects don't go to http://my_domain.com/test1 but they go to http://my_domain.com/
Is there a way, through nginx configurations, to tell the app that the root location is actually http://my_domain.com/test1?

I'm really new to nginx and to virtual hosts in general, i'm trying to learn... Any help would be appreciated.
EDIT:
The result of curl -I http://127.0.0.1:5000 is:

HTTP/1.1 200 OK
X-Powered-By: Express
Content-Type: text/html; charset=utf-8
Content-Length: 1376
ETag: W/"560-GGm/YYltkhKxiOVNZ99jqQ"
set-cookie: connect.sid=s%3AkZYCqLKvbhHhK3W8ECBN8G91s41paws4.ekLWefrd3NdQatT3VzFNozfnFs65YBEW9k9MNTdbQT0; Path=/; HttpOnly
Date: Sat, 15 Aug 2015 13:13:20 GMT
Connection: keep-alive  

As you can see i don't get a Location Header...
By the way, i managed to solve the problem using subdomains, that seem to work as i expected... Anyway an answer would be appreciated, since i might need it in the future.

Solution 1:

The only way I found to make this work is to use the HttpSubModule and adding sub_filter directives. Given your examples it could look like this:

sub_filter 'href="/' 'href="/test1/';
sub_filter "redirect('/')" "redirect('/test1/')";

Obviously the more specific your matching is the more options you'll have to add. If you go less specific, like just match "/ or '/ then you need less rules but run into the danger of substituting the wrong thing.

You probably also need to add:

sub_filter_types *;

so it doesn't just match text/html (which is the default) but also javascript and css files. Obviously * is the lazy approach which might break things and using specific mimetypes should be preferred.

Ultimately the correct way is to fix the web application. Most web frameworks support something like a base url/root url/url prefix (there doesn't seem to be standard name for this) which you can set to avoid exactly this problem.