Article
Mathematics
Giacomo Del Nin
Summary: The note demonstrates that for every measurable function on R-n, the set of points where the blowup exists and is not constant is (n-1)-rectifiable. In particular, for every u in L-loc(1)(R-n), the jump set J(u) is (n-1)-rectifiable.
ANNALI DELLA SCUOLA NORMALE SUPERIORE DI PISA-CLASSE DI SCIENZE
(2021)
Article
Mathematics
Filippo Cagnetti, Antonin Chambolle, Matteo Perugini, Lucia Scardia
Summary: This study provides an extension result for generalised special functions of bounded deformation and shows that a function in GSBD(p) with a small jump set coincides with a W-1,W-p function, up to a small set whose perimeter and volume are controlled by the size of the jump of the function.
JOURNAL OF CONVEX ANALYSIS
(2021)
Article
Engineering, Multidisciplinary
Xiangli Jiang, Guihua Xia, Zhiguang Feng, Qing-Long Han, Rong Su
Summary: This paper investigates the reachable set estimation for leaderless discrete-time homogeneous multiagent systems with general linear high-order dynamics and bounded exogenous disturbances. A protocol is designed using a Markov chain and gathering information from in-neighbors to ensure the stability and consensus of the system. The agreement dynamics are characterized using a nonsingular transformation, and it is proven that the intersection of reachable sets and agreement dynamics is nonempty.
IEEE TRANSACTIONS ON NETWORK SCIENCE AND ENGINEERING
(2023)
Article
Mathematics
Tristan C. Collins, Yang Li
Summary: This article studies a condition that an exact special Lagrangian N subset of C-n has a multiplicity one. When C is a special Lagrangian cone with a smooth, connected link and satisfies an integrability condition, the corresponding cylindrical tangent cone is unique. This result applies, for example, when C = C-HL(m) is the Harvey-Lawson Tm-1 cone for m≠8, 9.
GEOMETRIC AND FUNCTIONAL ANALYSIS
(2023)
Article
Mathematics, Applied
Huayou Xie, Chuanjiang Zhou, Yongjin Li
Summary: This note mainly focuses on orthogonality, examining properties and conditions of Birkhoff orthogonality, isosceles orthogonality, Pythagorean orthogonality, and approximate Birkhoff orthogonality perpendicular to B. The note establishes relations between linear functionals and hyperplanes through approximate Birkhoff orthogonality, and provides sufficient and necessary conditions for various types of orthogonality of bounded operators. Additionally, the note characterizes inner product spaces in terms of functional orthogonality.
AEQUATIONES MATHEMATICAE
(2023)
Article
Computer Science, Interdisciplinary Applications
Xianliang Liu, Zishen Yang, Wei Wang
Summary: This paper discusses the problem of finding a t-latency bounded strong target set with minimum cardinality in a given simple graph G. By proposing an inequality and specifying certain conditions, exact formulas for optimal solutions were derived.
JOURNAL OF COMBINATORIAL OPTIMIZATION
(2021)
Article
Mathematics
Gianni Dal Maso, Irene Fonseca, Giovanni Leoni
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY
(2018)
Article
Mathematics, Applied
Gianni Dal Maso, Christopher J. Larsen, Rodica Toader
JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES
(2019)
Article
Mathematics
Gianni Dal Maso, Rodica Toader
JOURNAL OF DIFFERENTIAL EQUATIONS
(2019)
Article
Mathematics, Applied
Gianni Dal Maso, Lucia De Luca
ADVANCES IN CALCULUS OF VARIATIONS
(2020)
Article
Mathematics, Applied
Filippo Cagnetti, Gianni Dal Maso, Lucia Scardia, Caterina Ida Zeppieri
ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE
(2019)
Article
Mathematics, Applied
Filippo Cagnetti, Gianni Dal Maso, Lucia Scardia, Caterina Ida Zeppieri
ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS
(2019)
Article
Mathematics, Applied
Gianni Dal Maso, Christopher J. Larsen, Rodica Toader
NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS
(2020)
Article
Mathematics, Applied
Gianni Dal Maso, Rodica Toader
CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS
(2020)
Article
Mathematics, Applied
Gianni Dal Maso, Francesco Sapio
Summary: The study focuses on the behavior of solutions to a viscoelastic model with long memory as the rate of change of data approaches zero, and it is proven that a rescaled version of the solutions converges to the solution of the corresponding stationary problem.
MILAN JOURNAL OF MATHEMATICS
(2021)
Article
Mathematics, Applied
Gianni Dal Maso, Rodica Toader
Summary: The properties of crack length in pressure-sensitive elasto-plastic materials in the planar case are studied, and it is proven that under suitable technical assumptions, the length is a pure jump function on the crack path.
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS
(2022)
Article
Mathematics
Filippo Cagnetti, Gianni Dal Maso, Lucia Scardia, Caterina Ida Zeppieri
Summary: In this paper, we investigate the deterministic and stochastic homogenisation of free-discontinuity functionals under linear growth and coercivity conditions. A novel aspect of our deterministic result is that it is based on very general assumptions on the integrands, which do not need to be periodic in the space variable. Combining this result with the pointwise Subadditive Ergodic Theorem, we establish a stochastic homogenisation result for stationary random integrands, characterising the limit integrands in terms of asymptotic cell formulas, similar to the classical periodic homogenisation case.
Article
Mathematics, Applied
Gianni Dal Maso, Rodica Toader
Summary: We introduce a new space of generalised functions with bounded variation to prove the existence of a solution to a minimum problem that arises in the variational approach to fracture mechanics in elastoplastic materials. We study the fine properties of the functions belonging to this space and prove a compactness result. In order to use the Direct Method of the Calculus of Variations we prove a lower semicontinuity result for the functional occurring in this minimum problem. Moreover, we adapt a nontrivial argument introduced by Friedrich to show that every minimizing sequence can be modified to obtain a new minimizing sequence that satisfies the hypotheses of our compactness result.
NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS
(2022)
Article
Mathematics, Applied
Gianni Dal Maso, Rodica Toader
Summary: We studied a variational model for crack growth in elasto-plastic materials with hardening in the antiplane case, and found the existence of a solution to the initial value problem with prescribed time-dependent boundary conditions.
ADVANCES IN CALCULUS OF VARIATIONS
(2022)
Article
Mathematics, Applied
Federico Cianci, Gianni Dal Maso
Summary: The study focuses on hyperbolic partial integro-differential systems in domains with time-dependent cracks, giving conditions that ensure the uniqueness of the solution with prescribed initial-boundary conditions and its continuous dependence on the cracks.
DIFFERENTIAL AND INTEGRAL EQUATIONS
(2021)
Article
Mathematics
Gianni Dal Maso, Luca Heltai
Summary: The study introduces a numerical implementation of a quasi-static crack growth model for linearly elastic-perfectly plastic materials, showing evidence of intermittent crack growth with jump characteristics that are influenced by material properties.
JOURNAL OF CONVEX ANALYSIS
(2021)
