Search results for "ANALISI"
showing 10 items of 1536 documents
Least Energy Solutions with Sign Information for Parametric Double Phase Problems
2022
We consider a parametric double phase Dirichlet problem. In the reaction there is a superlinear perturbation term which satisfies a weak Nehari-type monotonicity condition. Using the Nehari manifold method, we show that for all parameters below a critical value, the problem has at least three nontrivial solutions all with sign information. The critical parameter value is precisely identified in terms of the spectrum of the lower exponent part of the differential operator.
A remark on the radial minimizer of the Ginzburg-Landau functional
2014
Let Omega subset of R-2 be a bounded domain with the same area as the unit disk B-1 and letE-epsilon(u, Omega) = 1/2 integral(Omega) vertical bar del u vertical bar(2) dx + 1/4 epsilon(2) integral(Omega) (vertical bar u vertical bar(2) - 1)(2) dxbe the Ginzburg-Landau functional. Denote by (u) over tilde (epsilon) the radial solution to the Euler equation associated to the problem min {E-epsilon (u, B-1) : u vertical bar(partial derivative B1) = x} and byK = {v = (v(1), v(2)) is an element of H-1 (Omega; R-2) : integral(Omega) v(1) dx = integral(Omega) v(2) dx = 0,integral(Omega) vertical bar v vertical bar(2) dx >= integral(B1) vertical bar(u) over tilde vertical bar(2) dx}.In this note…
Optimal maps and exponentiation on finite dimensional spaces with Ricci curvature bounded from below
2013
We prove existence and uniqueness of optimal maps on $RCD^*(K,N)$ spaces under the assumption that the starting measure is absolutely continuous. We also discuss how this result naturally leads to the notion of exponentiation.
Rigidity and sharp stability estimates for hypersurfaces with constant and almost-constant nonlocal mean curvature
2018
We prove that the boundary of a (not necessarily connected) bounded smooth set with constant nonlocal mean curvature is a sphere. More generally, and in contrast with what happens in the classical case, we show that the Lipschitz constant of the nonlocal mean curvature of such a boundary controls its $C^2$-distance from a single sphere. The corresponding stability inequality is obtained with a sharp decay rate.
A rigidity problem on the round sphere
2015
We consider a class of overdetermined problems in rotationally symmetric spaces, which reduce to the classical Serrin's overdetermined problem in the case of the Euclidean space. We prove some general integral identities for rotationally symmetric spaces which imply a rigidity result in the case of the round sphere.
A sharp quantitative version of Alexandrov's theorem via the method of moving planes
2015
We prove the following quantitative version of the celebrated Soap Bubble Theorem of Alexandrov. Let $S$ be a $C^2$ closed embedded hypersurface of $\mathbb{R}^{n+1}$, $n\geq1$, and denote by $osc(H)$ the oscillation of its mean curvature. We prove that there exists a positive $\varepsilon$, depending on $n$ and upper bounds on the area and the $C^2$-regularity of $S$, such that if $osc(H) \leq \varepsilon$ then there exist two concentric balls $B_{r_i}$ and $B_{r_e}$ such that $S \subset \overline{B}_{r_e} \setminus B_{r_i}$ and $r_e -r_i \leq C \, osc(H)$, with $C$ depending only on $n$ and upper bounds on the surface area of $S$ and the $C^2$ regularity of $S$. Our approach is based on a…
The method of moving planes: a quantitative approach
2018
We review classical results where the method of the moving planes has been used to prove symmetry properties for overdetermined PDE's boundary value problems (such as Serrin's overdetermined problem) and for rigidity problems in geometric analysis (like Alexandrov soap bubble Theorem), and we give an overview of some recent results related to quantitative studies of the method of moving planes, where quantitative approximate symmetry results are obtained.
Convergence for varying measures in the topological case
2023
In this paper convergence theorems for sequences of scalar, vector and multivalued Pettis integrable functions on a topological measure space are proved for varying measures vaguely convergent.
Some perturbation results for quasi-bases and other sequences of vectors
2023
We discuss some perturbation results concerning certain pairs of sequences of vectors in a Hilbert space $\Hil$ and producing new sequences which share, with the original ones, { reconstruction formulas on a dense subspace of $\Hil$ or on the whole space}. We also propose some preliminary results on the same issue, but in a distributional settings.
Superlinear (p(z), q(z))-equations
2017
AbstractWe consider Dirichlet boundary value problems for equations involving the (p(z), q(z))-Laplacian operator in the principal part and prove the existence of one and three nontrivial weak solutions, respectively. Here, the nonlinearity in the reaction term is allowed to depend on the solution, but does not satisfy the Ambrosetti–Rabinowitz condition. The hypotheses on the reaction term ensure that the Euler–Lagrange functional, associated to the problem, satisfies both the -condition and a mountain pass geometry.