117,856 research outputs found
Atlante diplomatico del documento pontificio.
No full textSi presenta un campionario delle tipologie fondamentali della documentazione pontificia - Cancelleria, Segreteria -, affiancando ad ogni immagine trascrizione, datazione, regesto e commento diplomatico comprendente le informazioni di base su ciascun documento e sugli uffici di produzione
Fundamental solutions for Kolmogorov-Fokker-Planck operators with time-depending measurable coefficients
No full textWe consider a Kolmogorov-Fokker-Planck operator of the kind: (equation presented) where n ai j (t) oq i; j=1 is a symmetric uniformly positive matrix on Rq, q ≤ N, of bounded measurable coefficients defined for t 2 R and the matrix B = n bi j oN i; j=1 satisfies a structural assumption which makes the corresponding operator with constant ai j hypoelliptic. We construct an explicit fundamental solution Γ for L, study its properties, show a comparison result between Γ and the fundamental solution of some model operators with constant ai j, and show the unique solvability of the Cauchy problem for L under various assumptions on the initial datum
Harnack inequality for hypoelliptic ultraparabolic equations with a singular lower order term
No full textWe prove a Harnack inequality for the positive solutions of ultraparabolic equations of the type L u + V u = 0;where L is a linear second order hypoelliptic differential operator and V belongs to a class of functions of Stummel-Kato type. We also obtain the existence of a Green function and an uniqueness result for the Cauchy-Dirichlet problem
Dopo una rilettura dell’Alibrando
No full textIl contributo legge l poema di Albrando nella sua nota relazione con il dipinto di Polidoro da Caravaggio come un momento dello scontro tra francescani e domenicani sulla vendita delle indulgenze nella prima metà del XVI seolo.The paper reads Alibrando's poem in its known relationship with Polidoro da Caravaggio's painting as a moment of the fight between franciscans and dominicans on the selling of indulgenze in the first halfof 16th century
Pointwise local estimates and Gaussian upper bounds for a class of uniformly subelliptic ultraparabolic operators
No full textWe consider a set of smooth vector fields X_1,...,X_m and X0−∂t satisfying the Hoermander's hyipoellipticity condition, under the assumption that X_1,...,X_m and X0−∂t are invariant with respect to a suitable homogeneous Lie group. We consider the second order partial differential equations in divergence form, X_i (aij X_j) + X0−∂t, where A=(aij) is a bounded, symmetric and uniformly positive matrix with measurable coefficients, and we prove an L^infty source bound of the solution u in terms of its L^1 norm, by adaptingt the Moser's iterative methods to the non-Euclidean geometry of the Lie group.We then use a technique going back to Aronson to prove a pointwise upper bound of the fundamental solution of the operator X_i (aij X_j) + X0−∂t. The bound is given in terms of the value function of an optimal control problem related to the vector fields X_1,...,X_m and X0−∂t. Finally, by using the upper bound, the existence of a fundamental solution is then established for smooth coefficients aij
On Some Schroedinger type equations
No full textWe 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 clas
Harnack inequality and asymptotic lower bounds for the relativistic Fokker–Planck operator
No full textWe consider a class of second-order degenerate kinetic operators L in the framework of special relativity. We first describe L as a Hörmander operator which is invariant with respect to Lorentz transformations. Then we prove a Lorentz-invariant Harnack type inequality, and we derive accurate asymptotic lower bounds for positive solutions to L f = 0. As a consequence, we obtain a lower bound for the density of the relativistic stochastic process associated with L
Schauder type estimates for degenerate Kolmogorov equations with Dini continuous coefficients
No full textWe study the regularity properties of the second order linear operator in :
egin{equation*}
L u := sum_{j,k= 1}^{m} a_{jk}partial_{x_j x_k}^2 u + sum_{j,k= 1}^{N} b_{jk}x_k partial_{x_j} u - partial_t u,
end{equation*}
where are real valued matrices with constant coefficients, with symmetric and strictly positive. We prove that, if the operator satisfies H"ormander's hypoellipticity condition, and is a Dini continuous function, then the second order derivatives of the solution to the equation are Dini continuous functions as well. We also consider the case of Dini continuous coefficients 's. A key step in our proof is a Taylor formula for classical solutions to that we establish under minimal regularity assumptions on
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