A new class of nonhomogeneous differential operators and applications to anisotropic systems

作者：Boureanu Maria Magdalena

来源：Complex Variables and Elliptic Equations, 2016, 61(5): 712-730.

DOI：10.1080/17476933.2015.1114614

• nonhomogeneous differential operators
• anisotropic Sobolev spaces
• variable exponents
• elliptic systems
• critical points
• weak solutions
• existence
• uniqueness

We introduce a new class of operators that extend both generalized Laplace operators and generalized mean curvature operators. We start the discussion on general anisotropic systems with variable exponents that involve our operators, then we focus on a specific example of such system, we show that it admits a unique weak solution and we complete our work with some comments on other related systems. The newly introduced operators are appropriate for the study conducted in the anisotropic spaces with variable exponents, but at the end of the paper we also provide their versions corresponding to the studies conducted in the anisotropic Sobolev spaces with constant exponents, or in the isotropic variable exponent Sobolev spaces, since, to the best of our knowledge, they represent a novelty even for the classical Sobolev spaces.

• 出版日期2016-5-3