Search Results - "Solombrino, Francesco"
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Functionals Defined on Piecewise Rigid Functions: Integral Representation and Γ-Convergence
Published in Archive for rational mechanics and analysis (01-06-2020)“…We analyse integral representation and Γ -convergence properties of functionals defined on piecewise rigid functions , that is, functions which are piecewise…”
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Lower semicontinuity and relaxation for free discontinuity functionals with non-standard growth
Published in Calculus of variations and partial differential equations (2024)“…A lower semicontinuity result and a relaxation formula for free discontinuity functionals with non-standard growth in the bulk energy are provided. Our…”
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Integral representation and Γ-convergence for free-discontinuity problems with p(·)-growth
Published in Calculus of variations and partial differential equations (01-11-2023)“…An integral representation result for free-discontinuity energies defined on the space G S B V p ( · ) of generalized special functions of bounded variation…”
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Non-local approximation of the Griffith functional
Published in Nonlinear differential equations and applications (01-03-2021)“…An approximation, in the sense of Γ -convergence and in any dimension d ≥ 1 , of Griffith-type functionals, with p -growth ( p > 1 ) in the symmetrized…”
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A derivation of Griffith functionals from discrete finite-difference models
Published in Calculus of variations and partial differential equations (01-12-2020)“…We analyze a finite-difference approximation of a functional of Ambrosio–Tortorelli type in brittle fracture, in the discrete-to-continuum limit. In a suitable…”
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A multi-step Lagrangian scheme for spatially inhomogeneous evolutionary games
Published in Journal of evolution equations (01-06-2021)“…A multi-step Lagrangian scheme at discrete times is proposed for the approximation of a nonlinear continuity equation arising as a mean-field limit of…”
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On some non-local approximation of nonisotropic Griffith-type functionals
Published in Mathematics in engineering (01-01-2022)“…The approximation in the sense of $ \Gamma $-convergence of nonisotropic Griffith-type functionals, with $ p- $growth ($ p > 1 $) in the symmetrized gradient,…”
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Existence of minimizers of the Mumford-Shah functional with singular operators and unbounded data
Published in Annali di matematica pura ed applicata (01-06-2013)“…We consider the regularization of linear inverse problems by means of the minimization of a functional formed by a term of discrepancy to data and a…”
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Functionals Defined on Piecewise Rigid Functions: Integral Representation and $$\varGamma $$-Convergence
Published in Archive for rational mechanics and analysis (01-06-2020)Get full text
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Optimal control problems in transport dynamics with additive noise
Published in Journal of Differential Equations (15-11-2023)“…Motivated by the applications in leader-follower multi-agent dynamics, a class of optimal control problems is investigated, where the goal is to influence the…”
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Quasistatic Evolution in Perfect Plasticity for General Heterogeneous Materials
Published in Archive for rational mechanics and analysis (01-04-2014)“…Inspired by some recent developments in the theory of small-strain heterogeneous elastoplasticity, we both revisit and generalize the formulation of the…”
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Mean-Field Pontryagin Maximum Principle
Published in Journal of optimization theory and applications (01-10-2017)“…We derive a maximum principle for optimal control problems with constraints given by the coupling of a system of ordinary differential equations and a partial…”
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13
Well-posedness of Kolmogorov-Fokker-Planck equations with unbounded drift
Published in Journal of mathematical analysis and applications (15-03-2025)“…We consider Kolmogorov-Fokker-Planck equations with unbounded drift terms which are only measurable in time and locally Hölder continuous in space. In…”
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14
Radial solutions for a dynamic debonding model in dimension two
Published in Nonlinear analysis (01-06-2022)“…In this paper we deal with a debonding model for a thin film in dimension two, where the wave equation on a time-dependent domain is coupled with a flow rule…”
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15
Brittle membranes in finite elasticity
Published in Zeitschrift für angewandte Mathematik und Mechanik (01-11-2023)“…Abstract This work is devoted to the variational derivation of a reduced model for brittle membranes in finite elasticity. The main mathematical tools we…”
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16
Frustrated Ferromagnetic Spin Chains: A Variational Approach to Chirality Transitions
Published in Journal of nonlinear science (01-04-2015)“…We study the energy per particle of a one-dimensional ferromagnetic/antiferromagnetic frustrated spin chain with nearest and next-to-nearest interactions close…”
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Lower semicontinuity for functionals defined on piecewise rigid functions and on GSBD
Published in Journal of functional analysis (01-04-2021)“…In this work, we provide a characterization result for lower semicontinuity of surface energies defined on piecewise rigid functions, i.e., functions which are…”
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18
A priori time regularity estimates and a simplified proof of existence in perfect plasticity
Published in Mathematische Nachrichten (01-10-2015)“…We revisit the time‐incremental method for proving existence of a quasistatic evolution in perfect plasticity. We show how, as a consequence of a priori time…”
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A fractional approach to strain-gradient plasticity: beyond core-radius of discrete dislocations
Published in Mathematische annalen (21-10-2024)Get full text
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On global and local minimizers of prestrained thin elastic rods
Published in Calculus of variations and partial differential equations (01-08-2017)“…We study the stable configurations of a thin three-dimensional weakly prestrained rod subject to a terminal load as the thickness of the section vanishes. By Γ…”
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