Theory and Applications of Partial Differential Equations (Mathematical Concepts and Methods in Science and Engineering)  Piero Bassanini, Alan R. Elcrat, A. R. Elcrat, Angelo Miele, Elcrat, Alan R (1997) 

Plot 
This masterful text introduces firstyear graduate students to the basic ideas of the theory of partial differential equations in the context of the three fundamental equations of classical mathematical physics  the wave and heat equations and the Laplace equation. The authors avoid abstractions and succeed in demonstrating ideas by way of relatively simple, straightforward applications. Their book also deals with more advanced topics, including  the De GiorgiNashMoser theorem  nonlinear Dirichlet problems for elliptic equations  distributions and Sobolev spaces  and hyperbolic conservation laws in one space variable. 

