Variational differential inclusions without ellipticity condition

Abstract

The paper sets forth a new type of variational problem without any ellipticity or monotonicity condition. A prototype is a differential inclusion whose driving operator is the competing weighted $(p,q)$-Laplacian $-\Delta_p u+\mu\Delta_q u$ with $\mu\in \mathbb{R}$. Local and nonlocal boundary value problems fitting into this nonstandard setting are examined.

Keywords

• variational problem
• hemivariational inequality
• lack of ellipticity
• competing $(p
• q)$-laplacian
• local and nonlocal operators