Archivio della ricerca dell'Università di Modena e Reggio Emiliahttps://iris.unimore.itIl sistema di repository digitale IRIS acquisisce, archivia, indicizza, conserva e rende accessibili prodotti digitali della ricerca.Mon, 27 Sep 2021 04:48:54 GMT2021-09-27T04:48:54Z10691On the Cauchy problem for a non linear Kolmogorov equationhttp://hdl.handle.net/11380/421276Titolo: On the Cauchy problem for a non linear Kolmogorov equation
Abstract: We consider the Cauchy problem related to the partial differential equationLu ≡ Δ_x u + h(u)∂_y u − ∂_t u = f(·, u),where (x, y, t) ∈ R^N × R × ]0, T[, which arises in mathematical finance and in the theory of diffusion processes. We study the regularity of solutions regarding L as a perturbation of an operatorof Kolmogorov type. We prove the existence of local classical solutions and give some sufficient conditions for global existence.
Wed, 01 Jan 2003 00:00:00 GMThttp://hdl.handle.net/11380/4212762003-01-01T00:00:00ZMeeting "Kolmogorov Equations in Physics and Finance"http://hdl.handle.net/11380/644649Titolo: Meeting "Kolmogorov Equations in Physics and Finance"
Abstract: Probabilistic and analytical methods are fundamental in the modeling of physical and natural phenomena and in the description of financial markets.The purpose of this meeting is to highlight the new methods, directions and the most recent developments in the theories of Probability and Partial Differential Equations. Special emphasis will be placed on applications to Physics and Mathematical Finance. http://kolmogorov-2010.dm.unibo.it/
Fri, 01 Jan 2010 00:00:00 GMThttp://hdl.handle.net/11380/6446492010-01-01T00:00:00ZGeometric Methods in PDE ́s: I.N.d.A.M. Meeting on the occasion of the 70 th birthday of Ermanno Lanconelli, Cortona, 27-31 maggio 2013,http://hdl.handle.net/11380/1166837Titolo: Geometric Methods in PDE ́s: I.N.d.A.M. Meeting on the occasion of the 70 th birthday of Ermanno Lanconelli, Cortona, 27-31 maggio 2013,
Tue, 01 Jan 2013 00:00:00 GMThttp://hdl.handle.net/11380/11668372013-01-01T00:00:00ZA survey on the classical theory for Kolmogorov equationhttp://hdl.handle.net/11380/1200962Titolo: A survey on the classical theory for Kolmogorov equation
Abstract: We present a survey on the regularity theory for classic solutions to subelliptic degenerate Kolmogorov equations. In the last part of this note we present a detailed proof of a Harnack inequality and a strong maximum principle.
Wed, 01 Jan 2020 00:00:00 GMThttp://hdl.handle.net/11380/12009622020-01-01T00:00:00ZMultiplicity of solutions for laminar, fully-developed natural convection in inclined, parallel-plate channelshttp://hdl.handle.net/11380/1066455Titolo: Multiplicity of solutions for laminar, fully-developed natural convection in inclined, parallel-plate channels
Abstract: Natural convection in inclined channels is a rather common flow configuration: it occurs in solar energy systems, ventilated roofs as well as in many industrial applications and chemical processes. Analytical solutions for laminar, fully-developed natural convection in inclined parallel-plate channels are presented in this paper. The Boussinesq approximation is applied and viscous energy dissipation is neglected. One specific thermal configuration is addressed, where one wall is perfectly insulated and a constant, uniform heat flux is released to the fluid from the other wall. The resulting set of governing equations is non-linear, as the mean velocity is not assigned a priori but determined as part of the solution. Depending on the channel inclination angle and on the imposed heat flux conditions, either no solution, one solution, multiple or infinite solutions exist. Under restrictive assumptions velocity profiles are self-similar with respect to the channel inclination, while the temperature profile is independent of the inclination. The two-dimensional, hydraulically- and thermally-developing natural convection channel flow is simulated numerically for some combinations of channel inclination angle and heating intensity to identify the most physical between the many solutions.
Wed, 01 Jan 2014 00:00:00 GMThttp://hdl.handle.net/11380/10664552014-01-01T00:00:00ZHarnack inequalities and Lifting Procedure for Evolution Hypoelliptic Equationshttp://hdl.handle.net/11380/621235Titolo: Harnack inequalities and Lifting Procedure for Evolution Hypoelliptic Equations
Abstract: We consider, for any odd positive integer k, the degenerate Partial Differential Equationu_t = u_xx + x^k u_yand we prove a Harnack inequality which is expressed in terms of the integral curves of the vector fields that occur in the PDE. The novelty of our result is in that, as k>1, we cannot assume the existence of any Lie group in R^3 such that the vector fields are invariant. As an application of the Harnack inequality we prove a lower bond of the fundamental solution.
Tue, 01 Jan 2008 00:00:00 GMThttp://hdl.handle.net/11380/6212352008-01-01T00:00:00ZHarnack inequality and no-arbitrage bounds for self-financing portfolioshttp://hdl.handle.net/11380/616656Titolo: Harnack inequality and no-arbitrage bounds for self-financing portfolios
Abstract: We give a direct proof of the Harnack inequality for a class ofKolmogorov operators associated with a linear SDE and we find theexplicit expression of the optimal Harnack constant. We discuss somepossible implication of the Harnack inequality in Finance: specificallywe infer no-arbitrage bounds for the value of self-Financing portfoliosin terms of the initial wealth.
Thu, 01 Jan 2009 00:00:00 GMThttp://hdl.handle.net/11380/6166562009-01-01T00:00:00ZNon local Harnack inequalities for a class of partial differential equaitonshttp://hdl.handle.net/11380/618703Titolo: Non local Harnack inequalities for a class of partial differential equaitons
Abstract: We prove Gausian lower bounds for the Fundamental solution to a class of hypoelliptic PDE's. Our method relies on the repeated application of a Harnack inequality which is invariant woth respect to a suitable Lie group.
Thu, 01 Jan 2009 00:00:00 GMThttp://hdl.handle.net/11380/6187032009-01-01T00:00:00ZOn Some Schroedinger type equationshttp://hdl.handle.net/11380/618707Titolo: On Some Schroedinger type equations
Abstract: We prove a Harnack type inequality for positive solutions to the equation L u + V u = 0, where L is a degenerate Kolmogorov equation and V is a potential belonging to a Stummel-Kato class
Thu, 01 Jan 2009 00:00:00 GMThttp://hdl.handle.net/11380/6187072009-01-01T00:00:00ZSchauder estimates, Harnack inequality and Gaussian lower bound for Kolmogorov type operators in non-divergence formhttp://hdl.handle.net/11380/612316Titolo: Schauder estimates, Harnack inequality and Gaussian lower bound for Kolmogorov type operators in non-divergence form
Abstract: We prove Schauder type estimates and an invariant Harnack inequality for a class of degenerate evolution operators of Kolmogorov type. We also prove a Gaussian lower bound for the fundamental solution of the operator and a uniqueness result for the Cauchy problem. The proof of the lower bound is obtained by solving a suitable optimal control problem and using the invariant Harnack inequality.
Sun, 01 Jan 2006 00:00:00 GMThttp://hdl.handle.net/11380/6123162006-01-01T00:00:00Z