Partial Differential Equations with Variable Exponents

This book provides a thorough introduction to the theory of nonlinear PDEs with a variable exponent, particularly those of elliptic type. It presents the most important variational methods for elliptic PDEs described by nonhomogeneous differential operators and containing one or more power-type nonlinearities with a variable exponent. The authors give a systematic treatment of the basic mathematical theory and constructive methods for these classes of nonlinear elliptic equations as well as their applications to various processes arising in the applied sciences.