Functional Analysis, Sobolev Spaces and Partial Differential Equations

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Existence of entire solutions for a class of quasilinear elliptic equations (2013, background): “23 of [6] assures that Φλ is bounded from below in M and attains its infimum in M, i.”
Convex Optimization in Normed Spaces: Theory, Methods and Examples (2015, background): “For a comprehensive presentation, the reader is referred to [30] and [94].”
An Introduction to Nonlinear Functional Analysis and Elliptic Problems (2011, background): “The reader can found the details of the proofs in [1, 36, 58, 61, 88].”
An Inverse Result of Approximation by Sampling Kantorovich Series (2018, neutral): “Since the above equality holds for every Φ ∈ C∞ c (In), and f is continuous on R, it turns out that (see [10]): f(−y) − f(x̃ − y) = 0, y ∈ (−n, n).”
Partial Differential Equations (2018, neutral): “By continuity, b(z) = b(2) 2 z for all z ∈ R, that is, a(z) = a(2)−a(0) 2 z + a(0).”
NONSMOOTH ANALYSIS AND OPTIMIZATION (2017, neutral): “For example, the weak topological dual of L1(Ω) can be identi ed with L∞(Ω), with the duality pairing reducing to 〈v, v∗〉L1,L∞ = ∫ Ω v(x)v∗(x)dx, see, e.g., [Brezis 2010, ¿eorem 4.14].”
From nonlinear Fokker–Planck equations to solutions of distribution dependent SDE (2018, neutral): “, [11], p.”