IRIS Università degli Studi di Bolognahttps://cris.unibo.itIl sistema di repository digitale IRIS acquisisce, archivia, indicizza, conserva e rende accessibili prodotti digitali della ricerca.Wed, 23 Jun 2021 18:44:16 GMT2021-06-23T18:44:16Z10701Recent progresses on elliptic two-phase free boundary problemshttp://hdl.handle.net/11585/702760.2Titolo: Recent progresses on elliptic two-phase free boundary problems
Tue, 01 Jan 2019 00:00:00 GMThttp://hdl.handle.net/11585/702760.22019-01-01T00:00:00ZCharacterization by Asymptotic Mean Formulas of q−Harmonic Functions in Carnot Groupshttp://hdl.handle.net/11585/355117Titolo: Characterization by Asymptotic Mean Formulas of q−Harmonic Functions in Carnot Groups
Abstract: Aim of this paper is to extend the work (Ferrari et al. in Discrete Contin. Dyn. Syst. 34, 2779–2793, 2014) to the Carnot group setting. More precisely, we prove that in every Carnot group a function is q−harmonic (here 1 < q < ∞), if and only if it satisfies a particular asymptotic mean value formula.
Thu, 01 Jan 2015 00:00:00 GMThttp://hdl.handle.net/11585/3551172015-01-01T00:00:00ZHölder behavior of viscosity solutions of some fully nonlinear equations in the Heisenberg grouphttp://hdl.handle.net/11585/742818Titolo: Hölder behavior of viscosity solutions of some fully nonlinear equations in the Heisenberg group
Wed, 01 Jan 2020 00:00:00 GMThttp://hdl.handle.net/11585/7428182020-01-01T00:00:00ZRegularity Properties for a Class of Non-uniformly Elliptic Isaacs Operatorshttp://hdl.handle.net/11585/717637.2Titolo: Regularity Properties for a Class of Non-uniformly Elliptic Isaacs Operators
Wed, 01 Jan 2020 00:00:00 GMThttp://hdl.handle.net/11585/717637.22020-01-01T00:00:00ZPerron’s solutions for two-phase free boundary problems with distributed sourceshttp://hdl.handle.net/11585/505166Titolo: Perron’s solutions for two-phase free boundary problems with distributed sources
Abstract: We use Perron method to construct a weak solution to a two-phase free boundary problem with right-hand-side. We thus extend the results in Caffarelli (1988) for the homogeneous case.
Thu, 01 Jan 2015 00:00:00 GMThttp://hdl.handle.net/11585/5051662015-01-01T00:00:00ZMetric normal and curvatures in the Heisenberg group.http://hdl.handle.net/11585/40729Titolo: Metric normal and curvatures in the Heisenberg group.
Abstract: The metric normal is an useful tool to study geometric invariants of surfaces. In particular we can compute the horizontal
Hessian of the Carnot-Charath´eodory signed distance from a non-characteristic smooth surface in the Heisenberg group.
Moreover, as a byproduct, we obtain some new invariant objects associated with the notion of curvature of smooth
non-characteristic surfaces in the Heisenberg group. (Received September 06, 2006)
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Sun, 01 Jan 2006 00:00:00 GMThttp://hdl.handle.net/11585/407292006-01-01T00:00:00ZRegularity of the free boundary in two-phase Problems for linear elliptic operatorshttp://hdl.handle.net/11585/46779Titolo: Regularity of the free boundary in two-phase Problems for linear elliptic operators
Abstract: In this paper we complete the study of the regularity of the free boundary in two-phase problems for linear elliptic operators started in [M.C. Cerutti, F. Ferrari, S. Salsa, Two-phase problems for linear elliptic operators with variable coefficients: Lipschitz free boundaries are
C^{1,gamma} [Arch. Ration. Mech. Anal. 171 (2004) 329–348]. In particular we prove that Lipschitz and flat free boundaries (in a suitable sense) are smooth. As byproduct, we prove that Lipschitz free boundaries are smooth in the case of quasilinear operators of the form div(A(x,u)grad(u)) with Lipschitz coefficients.
Mon, 01 Jan 2007 00:00:00 GMThttp://hdl.handle.net/11585/467792007-01-01T00:00:00ZON THE HORIZONTAL MEAN CURVATURE FLOW FOR AXISYMMETRIC SURFACES IN THE HEISENBERG GROUPhttp://hdl.handle.net/11585/232470Titolo: ON THE HORIZONTAL MEAN CURVATURE FLOW FOR AXISYMMETRIC SURFACES IN THE HEISENBERG GROUP
Abstract: We study the horizontal mean curvature flow in the Heisenberg group by using the level-set method. We prove the uniqueness, existence and stability of axisymmetric viscosity solutions of the level-set equation. An explicit solution is given for the motion starting from a subelliptic sphere. We also give several properties of the level-set method and the mean curvature flow in the Heisenberg group.
Wed, 01 Jan 2014 00:00:00 GMThttp://hdl.handle.net/11585/2324702014-01-01T00:00:00ZThe Soap Bubble Theorem and a $ p $-Laplacian overdetermined problemhttp://hdl.handle.net/11585/714862.2Titolo: The Soap Bubble Theorem and a $ p $-Laplacian overdetermined problem
Wed, 01 Jan 2020 00:00:00 GMThttp://hdl.handle.net/11585/714862.22020-01-01T00:00:00ZTwo-phase problems with distributed sources: regularity of the free boundaryhttp://hdl.handle.net/11585/301920Titolo: Two-phase problems with distributed sources: regularity of the free boundary
Abstract: We investigate the regularity of the free boundary for a general class of two-phase free boundary problems with nonzero right-hand side. We prove that Lipschitz or flat free boundaries are C1,γ. In particular, viscosity solutions are indeed classical.
Wed, 01 Jan 2014 00:00:00 GMThttp://hdl.handle.net/11585/3019202014-01-01T00:00:00Z