21 citations · 35 across the 17 of their papers we have counts for
24 papers
Boundedness of Solutions to Nonlocal Systems
Serena Dipierro, João Gonçalves da Silva, Giorgio Poggesi +1
Under mild mass or energy assumptions, we prove uniform bounds for all distributional solutions of a multi-dimensional system of nonlocal semilinear equations. The setti…
Fractional De Giorgi conjecture in dimension 2 via complex-plane methods
Serena Dipierro, João Gonçalves da Silva, Giorgio Poggesi +1
We provide a new proof of the fractional version of the De Giorgi conjecture for the Allen-Cahn equation in for the full range of exponents. Our proof combines a met…
A quantitative Gidas-Ni-Nirenberg-type result for the -Laplacian via integral identities
Serena Dipierro, João Gonçalves da Silva, Giorgio Poggesi +1
We prove a quantitative version of a Gidas-Ni-Nirenberg-type symmetry result involving the -Laplacian. Quantitative stability is achieved here via integral identities based on t…
A general integral identity with applications to a reverse Serrin problem
Rolando Magnanini, Riccardo Molinarolo, Giorgio Poggesi
We prove a new general differential identity and an associated integral identity, which entails a pair of solutions of the Poisson equation with constant source term. This generali…
Quantitative stability for the nonlocal overdetermined Serrin problem
Serena Dipierro, Giorgio Poggesi, Jack Thompson +1
We establish quantitative stability for the nonlocal Serrin overdetermined problem, via the method of the moving planes. Interestingly, our stability estimate is even better than t…
Quantitative stability for overdetermined nonlocal problems with parallel surfaces and investigation of the stability exponents
Serena Dipierro, Giorgio Poggesi, Jack Thompson +1
In this article, we analyze the stability of the parallel surface problem for semilinear equations driven by the fractional Laplacian. We prove a quantitative stability result that…
Remarks about the mean value property and some weighted Poincaré-type inequalities
Giorgio Poggesi
We start providing a quantitative stability theorem for the rigidity of an overdetermined problem involving harmonic functions in a punctured domain. Our approach is inspired by an…
Quantitative symmetry in a mixed Serrin-type problem for a constrained torsional rigidity
Rolando Magnanini, Giorgio Poggesi
We consider a mixed boundary value problem in a domain contained in a half-ball and having a portion of its boundary in common with the curved part of $\partial…
The role of antisymmetric functions in nonlocal equations
Serena Dipierro, Giorgio Poggesi, Jack Thompson +1
We prove a Hopf-type lemma for antisymmetric super-solutions to the Dirichlet problem for the fractional Laplacian with zero-th order terms. As an application, we use such a Hopf-t…
Symmetry and quantitative stability for the parallel surface fractional torsion problem
Giulio Ciraolo, Serena Dipierro, Giorgio Poggesi +2
We study symmetry and quantitative approximate symmetry for an overdetermined problem involving the fractional torsion problem in a bounded domain . More prec…
Interpolating estimates with applications to some quantitative symmetry results
Rolando Magnanini, Giorgio Poggesi
We prove interpolating estimates providing a bound for the oscillation of a function in terms of two norms of its gradient. They are based on a pointwise bound of a function…
Quantitative stability estimates for a two-phase Serrin-type overdetermined problem
Lorenzo Cavallina, Giorgio Poggesi, Toshiaki Yachimura
In this paper, we deal with an overdetermined problem of Serrin-type with respect to a two-phase elliptic operator in divergence form with piecewise constant coefficients. In parti…
Radial symmetry of solutions to anisotropic and weighted diffusion equations with discontinuous nonlinearities
Serena Dipierro, Giorgio Poggesi, Enrico Valdinoci
We prove radial symmetry for bounded nonnegative solutions of a weighted anisotropic problem. Given the anisotropic setting that we deal with, the term "radial" is understood in th…
A quantitative rigidity result for a two-dimensional Frenkel-Kontorova model
Serena Dipierro, Giorgio Poggesi, Enrico Valdinoci
We consider a Frenkel-Kontorova system of harmonic oscillators in a two-dimensional Euclidean lattice and we obtain a quantitative estimate on the angular function of the equilibri…
The location of hot spots and other extremal points
Rolando Magnanini, Giorgio Poggesi
In a domain of the Euclidean space, we estimate from below the distance to the boundary of global maximum points of solutions of elliptic and parabolic equations with homogeneous D…
A Serrin-type problem with partial knowledge of the domain
Serena Dipierro, Giorgio Poggesi, Enrico Valdinoci
We present a quantitative estimate for the radially symmetric configuration concerning a Serrin-type overdetermined problem for the torsional rigidity in a bounded domain , when…
An interpolating inequality for solutions of uniformly elliptic equations
Rolando Magnanini, Giorgio Poggesi
We extend an inequality for harmonic functions, obtained in previous research by the authors, to the case of solutions of uniformly elliptic equations in divergence form, with mere…
Nearly optimal stability for Serrin's problem and the Soap Bubble theorem
Rolando Magnanini, Giorgio Poggesi
We present new quantitative estimates for the radially symmetric configuration concerning Serrin's overdetermined problem for the torsional rigidity, Alexandrov's Soap Bubble Theor…
The Soap Bubble Theorem and Serrin's problem: quantitative symmetry
Giorgio Poggesi
This PhD thesis was defended on 18 February 2019 at Università di Firenze.
Stable solutions to some elliptic problems: minimal cones, the Allen-Cahn equation, and blow-up solutions
Xavier Cabre, Giorgio Poggesi
These notes record the lectures for the CIME Summer Course taught by the first author in Cetraro during the week of June 19-23, 2017. The notes contain the proofs of several result…
Radial symmetry for p-harmonic functions in exterior and punctured domains
Giorgio Poggesi
We prove symmetry for the p-capacitary potential satisfying $$ Δ_p u = 0 \, \mbox{ in } \mathbb{R}^N \setminus \overlineΩ , \; u=1 \, \mbox{ on } Γ, \; \lim_{|x|\rightarrow \infty}…
Serrin's problem and Alexandrov's Soap Bubble Theorem: enhanced stability via integral identities
Rolando Magnanini, Giorgio Poggesi
We consider Serrin's overdetermined problem for the torsional rigidity and Alexandrov's Soap Bubble Theorem. We present new integral identities, that show a strong analogy between…
On the stability for Alexandrov's Soap Bubble theorem
Rolando Magnanini, Giorgio Poggesi
Alexandrov's Soap Bubble theorem dates back to and states that a compact embedded hypersurface in with constant mean curvature must be a sphere. For its proof…
Littlewood's fourth principle
Rolando Magnanini, Giorgio Poggesi
In Real Analysis, Littlewood's three principles are known as heuristics that help teach the essentials of measure theory and reveal the analogies between the concepts of topologica…