For a developer with a Java background, I am interested in exploring software development using the ASP.NET tools/platform as well.
Java web applications (.jsp and servlets) can run on many server platforms.
Question: Will a .NET web application be able to run in a Linux based server? Considering the scenario of not being able to use a Windows server for hosting a web app.
It depends what specific .NET technologies you're using. The Mono Project provides an Apache module (mod_mono) for running ASP.NET sites, and from what I gather it works well.
Mono doesn't support all the .NET APIs, though - notably WPF (and possibly WCF too, I can't remember) - but it does provide good support for much else of the framework.
If you're starting from scratch and particularly want to target non-Windows servers, then ensuring your project works with Mono would be a good goal to aim for. However, if you need particular APIs or language features that are not supported by Mono, then you will need to use a Windows server for deployment. It's a design-time/architectural choice that should make up front.