maxwell's equation and boundary conditions?

Answer 1

Maxwell's Equations
Maxwell's equations represent one of the most elegant and concise ways to state the fundamentals of electricity and magnetism. From them one can develop most of the working relationships in the field. Because of their concise statement, they embody a high level of mathematical sophistication and are therefore not generally introduced in an introductory treatment of the subject, except perhaps as summary relationships.
These basic equations of electricity and magnetism can be used as a starting point for advanced courses, but are usually first encountered as unifying equations after the study of electrical and magnetic phenomena.

Answer 2

What is your question? When you solve them for a particular set of conditions, the solution must be valid at the boundaries as well as throughout the space.