1,721,014 research outputs found
Improved bounds for Hermite-Hadamard inequalities in higher dimensions
No full textLet be a convex domain and let be a positive, subharmonic function (i.e. ). Then where . This inequality was previously only known for convex functions with a much larger constant. We also show that the optimal constant satisfies . As a byproduct, we establish the following sharp geometric inequality for two convex domains where one contains the other : rac{|partial Omega_1|}{|Omega_1|} rac{| Omega_2|}{|partial Omega_2|} leq n.$
On a time-depending Monge-Ampère type equation
No full textIn this paper, we prove a comparison result between a solution u(x, t), x is an element of Omega subset of R-2, t is an element of (0, T), of a time depending equation involving the Monge-Ampere operator in the plane and the solution of a conveniently symmetrized parabolic equation. To this aim, we prove a derivation formula for the integral of a smooth function g(x, t) over sublevel sets of u, {x is an element of Omega : u(x, t) < nu}, nu is an element of R, having the same perimeter in R-2. (C) 2012 Elsevier Ltd. All rights reserved
On the symmetry of solutions to a k-Hessian type equation
No full textIn this note we prove that if u is a negative solution to a nonlinear elliptic equation involving a Hessian operator, and u is zero on the boundary of a ball, then u is radially symmetric and increasing along the radii
Comparison results for Monge - Ampère type equations with lower order terms
No full textIn this paper we deal with Monge-Ampère type equations in two dimensions and, using the symmetrization with respect to the perimeter, we prove some comparison results for solutions of such equations involving the solutions of conveniently symmetrized problems
I poligoni: dai mosaici dell’Alhambra alle incisioni di Escher
No full textDescrizione delle attività svolte durante l'omonimo laboratorio tenuto per il PLS matematica nell'anno 201
Existence and comparison results for a singular semilinear elliptic equation with a lower order term
No full textThis paper deals with the homogeneous Dirichlet problem for a singular semilinear elliptic equation with a first order term. When the datum is bounded we prove an existence result and we show that any solution can be compared with the solution to a suitable symmetrized problem
A sharp estimate for Neumann eigenvalues of the Laplace-Beltrami operator for domains in a hemisphere
Full text linkHere, we prove an isoperimetric inequality for the harmonic mean of the first N - 1 non-trivial Neumann eigenvalues of the Laplace-Beltrami operator for domains contained in a hemisphere of N
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