Showing papers in "Revista Matematica Complutense in 2023"

Multiple solutions for nonlinear boundary value problems of Kirchhoff type on a double phase setting

Abstract: Abstract This paper deals with some classes of Kirchhoff type problems on a double phase setting and with nonlinear boundary conditions. Under general assumptions, we provide multiplicity results for such problems in the case when the perturbations exhibit a suitable behavior in the origin and at infinity, or when they do not necessarily satisfy the Ambrosetti–Rabinowitz condition. To this aim, we combine variational methods, truncation arguments and topological tools.

Algebraic valuation ring extensions as limits of complete intersection algebras

Abstract: We show that an algebraic immediate valuation ring extension of characteristic $$p>0$$ is a filtered union of complete intersection algebras of finite type.

Strict $${\mathcal {C}}^p$$-triangulations of sets locally definable in o-minimal structures with an application to a $$\mathcal C^p$$-approximation problem

Abstract: Abstract We show how to derive triangulations of sets locally definable in o-minimal structures from triangulations of compact definable sets. We give it in particular for strict $$\mathcal C^p$$ C p -triangulations which has been recently studied by the author. This combined with a theorem of Fernando and Ghiloni implies that every continuous mapping defined on a locally compact subset B of $$\mathbb R^m$$ R m with values in any locally definable and locally compact subset A of $$\mathbb R^n$$ R n can be approximated by $$\mathcal C^p$$ C p -mappings defined on B with values in A for any positive integer p .

New examples of harmonic maps to the hyperbolic plane via Bäcklund transformation

Abstract: Abstract We study harmonic maps from a subset of the complex plane to a subset of the hyperbolic plane. In Fotiadis and Daskaloyannis (Nonlinear Anal 214, 112546, 2022), harmonic maps are related to the sinh-Gordon equation and a Bäcklund transformation is introduced, which connects solutions of the sinh-Gordon and sine-Gordon equation. We develop this machinery in order to construct new harmonic maps to the hyperbolic plane.

Critical metrics for quadratic curvature functionals on some solvmanifolds

Abstract: Abstract We prove the existence of four-dimensional compact manifolds admitting some non-Einstein Lorentzian metrics, which are critical points for all quadratic curvature functionals. For this purpose, we consider left-invariant semi-direct extensions $$G_{\mathcal S}=H \rtimes \exp ({\mathbb {R}}S)$$ G S = H ⋊ exp ( R S ) of the Heisenberg Lie group H , for any $$\mathcal S \in {\mathfrak {s}}{\mathfrak {p}}(1,\mathbb R)$$ S ∈ s p ( 1 , R ) , equipped with a family $$g_a$$ g a of left-invariant metrics. After showing the existence of lattices in all these four-dimensional solvable Lie groups, we completely determine when $$g_a$$ g a is a critical point for some quadratic curvature functionals. In particular, some four-dimensional solvmanifolds raising from these solvable Lie groups admit non-Einstein Lorentzian metrics, which are critical for all quadratic curvature functionals.

Variable exponent Sobolev spaces and regularity of domains-II

Abstract: Abstract We provide necessary conditions on Euclidean domains for inclusions $$W^{1,p(\cdot )}(\Omega ) \hookrightarrow L^{q(\cdot )}(\Omega ) $$ W 1 , p ( · ) ( Ω ) ↪ L q ( · ) ( Ω ) of variable exponent Sobolev spaces. The conditions on the exponent $$ p(\cdot ) $$ p ( · ) are log-Hölder and log-log-Hölder continuity, while those on the domain $$ \Omega $$ Ω are the measure and the log measure density conditions. Restrictions on the exponents $$ q(\cdot ) $$ q ( · ) and $$ p(\cdot )$$ p ( · ) appearing in Górka et al. (J. Geom. Anal. 310: 7304-7319, 2021) are relaxed, improving the results obtained in that work.

Terracini loci of curves

Abstract: Abstract We study subsets S of curves X whose double structure does not impose independent conditions to a linear series L , but there are divisors $$D\in |L|$$ D ∈ | L | singular at all points of S. These subsets form the Terracini loci of X . We investigate Terracini loci, with a special look towards their non-emptiness, mainly in the case of canonical curves, and in the case of space curves.

Equivalent characterizations of martingale Hardy–Lorentz spaces with variable exponents

Abstract: Abstract We prove that under the log-Hölder continuity condition of the variable exponent $$p(\cdot )$$ p ( · ) , a new type of maximal operators, $$U_{\gamma ,s}$$ U γ , s is bounded from the variable martingale Hardy–Lorentz space $$H_{p(\cdot ),q}$$ H p ( · ) , q to $$L_{p(\cdot ),q}$$ L p ( · ) , q , whenever $$0<p_-\le p_+ <\infty $$ 0 < p - ≤ p + < ∞ , $$0<q \le \infty $$ 0 < q ≤ ∞ , $$0<\gamma ,s<\infty $$ 0 < γ , s < ∞ and $$1/p_- - 1/p_+ < \gamma +s$$ 1 / p - - 1 / p + < γ + s . Moreover, the operator $$U_{\gamma ,s}$$ U γ , s generates equivalent quasi-norms on the Hardy–Lorentz spaces $$H_{p(\cdot ),q}$$ H p ( · ) , q .

Ranks of maps of vector bundles

Abstract: We generalize to vector bundles the techniques introduced for line bundles in prior work of the author with Liu, Osserman and Zhang. We then use this method to prove the injectivity of the Petri map for vector bundles and the surjectivity of a map related to deformation theory of Poincar\'e sheaves.