Make sure that the -L option appears ahead of the -l option; the order of options in linker command lines does matter, especially with static libraries. The -L option specifies a directory to be searched for libraries (static or shared). The -lname option specifies a library which is with libmine.a (static) or libmine.so (shared on most variants of Unix, but Mac OS X uses .dylib and HP-UX used to use .sl). Conventionally, a static library will be in a file libmine.a. This is convention, not mandatory, but if the name is not in the libmine.a format, you cannot use the -lmine notation to find it; you must list it explicitly on the compiler (linker) command line.
The -L./libmine option says "there is a sub-directory called libmine which can be searched to find libraries". I can see three possibilities:
libmine.a, in which case you also need to add -lmine to the linker line (after the object files that reference the library).libmine that is a static archive, in which case you simply list it as a file ./libmine with no -L in front. libmine.a in the current directory that you want to pick up. You can either write ./libmine.a or -L . -lmine and both should find the library.