List of publications

Hamilton-Jacobi equations and optimal control problems
  1. Semiconcavity of solutions of stationary Hamilton-Jacobi equations, Nonlinear Analysis TMA  24, 1321-1326 (1995).
  2. (with P. Cannarsa) Convexity properties of the minimum time function, Calculus of Variations and Partial Differential Equations  3 273-298 (1995).
  3. (with P. Cannarsa) On a class of nonlinear time optimal control problems, Discrete and Continuous Dynamical Systems  1 285-300 (1995).
  4. Local regularity properties of the minimum time function, in PDE Methods in Control Problems, Shape Optimization and Stochastic Problems (Pisa, 1994) , Marcel Dekker, Lecture Notes in Pure and Applied Mathematics 188 (1997).
  5. (with P. Cannarsa and A. Mennucci) Regularity results for solutions of a class of Hamilton-Jacobi equations, Archive for Rational Mechanics and Analysis  140 197-223 (1997).
  6. (with P. Cannarsa) An infinite dimensional time optimal control problem, in Optimization Methods in Partal Differential Equations (M. Holyoke, USA, 1996)  A.M.S. Contemporary Mathematics 209 (1997).
  7. Layering methods for Hamilton-Jacobi equations with nonconvex hamiltonian, Nonlinear Analysis TMA  38 137-149 (1999).
  8. (with E. Barron, P. Cannarsa and R. Jensen) Regularity of Hamilton-Jacobi equations when forward is backward, Indiana University Mathematics Journal   48 385-409 (1999).
  9. (with P. Albano and P. Cannarsa) Regularity results for the minimum time function of a class of semilinear evolution equations of parabolic type, SIAM Journal of Control and Optimization , 38 916-946 (2000).
  10. (with P. Cannarsa and H. Frankowska) Optimality conditions and synthesis for the minimum time problem, Set-Valued Analysis, 8 127-148 (2000).
  11. (with P. Cannarsa and C. Pignotti) Semiconcavity for optimal control problem with exit time, Discrete and Continuous Dynamical Systems , 6 975-997 (2000).
  12. (with P. Cannarsa) Semiconcave functions, Hamilton-Jacobi equations and optimal control problems, (Progress in Nonlinear Differential Equations and Their Applications, 58 ) Birkhäuser Boston, (2004) ISBN: 0-8176-4084-3 (hardcover) ISBN: 0-8176-4336-2 (softcover).
  13. Regularity along optimal trajectories of the value function of a Mayer problem , ESAIM Control, Optimisation and Calculus of Variations 10 666-676 (2004).
  14. Semiconcavity of the value function for exit time problems with nonsmooth target , Communications in Pure and Applied Analysis 3 757-774 (2004).
  15. (with P. Cannarsa and P. Cardaliaguet) On a differential model for growing sandpiles with non-regular sources, Communications in Partial Differential Equations 34 656-675 (2009).
  16. (with P. Albano, P. Cannarsa and Khai T. Nguyen) Singular gradient flow of the distance function and homotopy equivalence. Mathematische Annalen 356 23-43 (2013).
  17. (with M. Mazzola and P. Cannarsa) Global propagation of singularities for time dependent Hamilton-Jacobi equation , Discrete and Continuous Dynamical Systems, Series A 35 4225-4239 (2015).
  18. (with F. Alabau, F. Ancona and A. Porretta, Editors) Trends in control theory and partial differential equations. Springer INdAM series, n. 32. Springer Nature Switzerland (2019).
  19. (with P. Albano and P. Cannarsa) Generation of singularities from the initial datum for Hamilton-Jacobi equations , Journal of Differential Equations , 268 1412-1426 (2020), also available on arXiv:1907.00796.
Geometric flows
  1. (with G. Huisken) Mean curvature flow singularities for mean convex surfaces, Calculus of Variations and Partial Differential Equations  8 1-14 (1999).
  2. (with G. Huisken) Convexity estimates for mean curvature flow and singularities of mean convex surfaces, Acta Mathematica  183 45-70 (1999).
  3. Singularities of mean curvature flow and flow with surgeries, in Surveys in Differential Geometry Volume 12: Geometric Flows (H.D. Cao, S.T. Yau, Editors), International Press, Boston (2008).
  4. (with G. Huisken) Mean curvature flow with surgeries of two-convex hypersurfaces, Inventiones Mathematicae 175 137-221 (2009).
  5. (with M. Ritoré) Mean curvature flow and isoperimetric inequalities (V. Miquel and J. Porti, eds.). Birkhäuser (2010).
  6. (with R. Alessandroni) Convexity estimates for a nonhomegenous mean curvature flow , Mathematische Zeitschrift 266 65-82 (2010).
  7. (with E. Cabezas Rivas), Volume-preserving flow by powers of the m-th mean curvature, Calculus of Variations and Partial Differential Equations , 38 441-469 (2010).
  8. (with R. Alessandroni) Evolutions of hypersurfaces by powers of the scalar curvature, Annali della Scuola Normale Superiore di Pisa , 9 541-571 (2010).
  9. (with S. Brendle and G. Huisken) Ancient solutions to the Ricci flow with pinched curvature, Duke Mathematical Journal , 158 537-551 (2011), available on arXiv.
  10. (with G. Huisken) Convex ancient solutions of the mean curvature flow , Journal of Differential Geometry , 101 267-287 (2015).
  11. Convex hypersurfaces evolving by volume preserving curvature flows Calculus of Variations and Partial Differential Equations , 54 1985-1993 (2015), the preprint version is available here .
  12. (with R. Alessandroni) Evolution of convex entire graphs by curvature flows Geometric Flows , 1 111-125 (2015).
  13. (with M. Boileau, G. Besson and G. Tian) Ricci flow and geometric applications (R. Benedetti, C. Mantegazza Eds.), C.I.M.E. Foundation Subseries, Springer (2016).
  14. (with G. Pipoli) Cylindrical estimates for mean curvature flowof hypersurfaces in CROSSes, Annals of Global Analysis and Geometry , 51 , 179-188 (2017).
  15. (with G. Pipoli) Mean curvature flow of pinched submanifolds of CP^n , Communications in Analysis and Geometry 25 , 799-846 (2017), available on arXiv .
  16. (with E. Cinti and E. Valdinoci) Neckpinch singularities in fractional mean curvature flows, Proceedings of the American Mathematical Society , 146 , 2637-2646 (2018), also available on arXiv .
  17. (with M.C. Bertini) Volume preserving non homogeneous mean curvature flow of convex hypersurfaces , Annali di Matematica Pura ed Applicata , 197 , 1295-1309, (2018). also available on arXiv .
  18. (with M.C. Bertini) Volume preserving flow by powers of symmetric polynomials in the principal curvatures , Mathematische Zeitschrift , 289 , 1219-1236, (2018), also available on arXiv .
  19. (with S. Risa) Ancient solutions of geometric flows with curvature pinching , The Journal of Geometric Analysis , 29 , 1206-1232, (2019).
  20. (with S. Risa) Strong spherical rigidity of ancient solutions of expansive curvature flows , Bulletin of the London Mathematical Society , 52 , 94-99 (2020), also available on arXiv .
  21. (with E. Cinti and E. Valdinoci) Convex sets evolving by volume preserving fractional mean curvature flows, Analysis and PDEs , 13 , 2149-2171 (2020), also available on arXiv and on cvgmt .
  22. (with S. Risa) Non-homothetic convex ancient solutions for flows by high powers of curvature, preprint (2022), arXiv:2203.05259 .
Hyperbolic conservation laws
  1. Large time behaviour of solutions of balance laws with periodic initial data, Nonlinear Differential Equations and Applications  2 111-131 (1995).
  2. Asymptotic profile of solutions of conservation laws with source, Differential and Integral Equations  9 499-525 (1996).
  3. (with R. Natalini and A. Tesei) Incomplete blowup of solutions of quasilinear hyperbolic balance laws, Archive for Rational Mechanics and Analysis  135 259-296 (1996).
  4. The Riemann problem for an inhomogeneous conservation law without convexity, SIAM Journal for Mathematical Analysis  28 109-135 (1997).
  5. Instability of discontinuous traveling waves for hyperbolic balance laws, Journal of Differential Equations  134 269-285 (1997).
  6. (with C. Mascia) The perturbed Riemann problem for a balance law, Advances in Differential Equations  2 779-810 (1997).
  7. (with H. K. Jenssen) Blowup for hyperbolic equations, in Hyperbolic Problems: Theory, Numerics, Applications (Zürich, 1998), Birkhäuser ISNM 129 (1999).
  8. (with H. K. Jenssen) Blowup asymptotics for scalar conservation laws with a source, Communications in Partial Differential Equations 11-12 2237-2261 (1999).
  9. (with H. K. Jenssen) On the spreading of characteristics for nonconvex conservation laws, Proceedings of the Royal Society of Edinburgh 131 909-925 (2001).

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