Sobolev Spaces: with Applications to Elliptic Partial Differential Equations

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On the First Eigenvalues of Free Vibrating Membranes in Conformal Regular Domains (2015, background): “The first non-trivial eigenvalue of the Neumann–Laplace operator is connected to the sharp constants in the isoperimetric inequalities [25].”
Caffarelli–Kohn–Nirenberg type inequalities of fractional order with applications (2016, background): “Statement and proof of the main results Let us begin with some functional settings that will be used below, we refer to [12] and [22] for more details.”
Nonlocal self-improving properties (2015, unknown): “We recall that the fractional Sobolev space W s,γ , for γ ≥ 1 and s ∈ (0, 1), is given by the subspace of L(R)functions u such that the following Gagliardo seminorm is finite (see for instance [11, 21]) (1.”
Manifold Constrained Non-uniformly Elliptic Problems (2019, unknown): “Classical reference in this respect are [11, 28, 37, 49, 51].”