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In this work, a subclass of the generalized Kerr-Schild class of spacetimes is specified, with respect to which the Ricci tensor (regardless of the position of indices) proves to be linear in the so-called profile function of the geometry.…
In this work it is studied a quasilinear elliptic problem in the whole space $\mathbb{R}^N$ involving the $1-$Laplacian operator, with potentials which can vanish at infinity. The Euler-Lagrange functional is defined in a space whose…
We establish an existence result of a solution to a class of probability measure-valued equations, whose solutions can be associated with stationary distributions of many McKean-Vlasov diffusions with gradient-type drifts. Coefficients of…
We consider the behaviour of holomorphic functions on a bounded open subset of the plane, satisfying a Lipschitz condition with exponent $\alpha$, with $0<\alpha<1$, in the vicinity of an exceptional boundary point where all such functions…
In this work we consider natural generalizations of local complementation in Banach spaces, which include Lipschitz-local complementation. We show that all these notions are indeed equivalent to the classical notion of local complementation…
We consider the linear elliptic systems or equations in divergence form with periodically oscillating coefficients. We prove the large-scale boundary Lipschitz estimate for the weak solutions in domains satisfying the so-called…
The article introduces Ahlfors' generalization of the Schwarz lemma. With this powerful geometric tool of complex functions in one variable, we are able to prove some theorems concerning the size of images under holomorphic mappings,…
We generalize the classical Blaschke Rolling Theorem to convex domains in Riemannian manifolds of bounded sectional curvature and arbitrary dimension. Our results are sharp and, in this sharp form, are new even in the model spaces of…
The vacuum transition probabilities between to minima of a scalar field potential in the presence of gravity are studied using the Wentzel-Kramers-Brillouin approximation. First we propose a method to compute these transition probabilities…
In this paper, we provide a generalization of the forward-backward splitting algorithm for minimizing the sum of a proper convex lower semicontinuous function and a differentiable convex function whose gradient satisfies a locally…
The study on the partial differential equations (systems) in the graph setting is a hot topic in recent years because of their applications to image processing and data clustering. Our motivation is to develop some existence results for…
We provide integral representation and $\Gamma$-compactness results for anisotropic local functionals depending on arbitrary Lipschitz continuous vector fields. In particular, neither bracket-generating assumptions nor linear independence…
We initiate a program of average smoothness analysis for efficiently learning real-valued functions on metric spaces. Rather than using the Lipschitz constant as the regularizer, we define a local slope at each point and gauge the function…
We provide an extension of the Hartman-Knobloch theorem for periodic solutions of vector differential systems to a general class of $\phi$-Laplacian differential operators. Our main tool is a variant of the Man\'{a}sevich-Mawhin…
The main contribution of this paper is that every convex function with non-empty relative algebraic interior of its domain is Lipschitz and subdifferentiable in some algebraic sense without any additional topological constraints. The…
Decentralized optimization has become a fundamental tool for large-scale learning systems; however, most existing methods rely on the classical Lipschitz smoothness assumption, which is often violated in problems with rapidly varying…
We develop a gradient-flow theory for time-dependent functionals defined in abstract metric spaces. Global well-posedness and asymptotic behavior of solutions are provided. Conditions on functionals and metric spaces allow to consider the…
A recent theorem of Bissacot, et al. proved using results about the cluster expansion in statistical mechanics extends the Lov\'asz Local Lemma by weakening the conditions under which its conclusions holds. In this note, we prove an…
Using the notion of modulus of continuity at a point of a mapping between metric spaces, we introduce the notion of extensively bounded mappings generalizing that of Lipschitz mappings. We also introduce a metric on it which becomes a norm…
Generalized smooth functions are a possible formalization of the original historical approach followed by Cauchy, Poisson, Kirchhoff, Helmholtz, Kelvin, Heaviside, and Dirac to deal with generalized functions. They are set-theoretical…