1,720,993 research outputs found
Comparison results for solutions of parabolic equations
No full textWe state comparison results between solutions of the Cauchy-Dirichlet problem for a class of linear parabolic equations and solutions of a suitable "symmetrized" problem
Convex rearrangement: equality cases in the Pòlya-Szegö inequality
No full textIt is known that for any nonnegative function u compactly supported in R^n ∫(H(Du))^2 dx≥∫(H(Du^*))^2 dx where H is a nonnegative convex function, positively homogeneous of degree 1 and u^* is the "convex" rearrangement of u with respect to H. We deal with the problem of characterizing those functions u for which equality holds
Comparison results for solutions of parabolic equations with a singular potential
No full textWe consider the solution u of the Cauchy-Dirichlet problem for a class of linear parabolic equations in which the coefficient of the zero order term could have a singularity at the origin of the type 1/|x|^2. We prove that u can be compared "in the sense of rearrangements" with the solution of a problem whose data are radially symmetric with respect to the space variable
An inequality concerning rearrangements of functions
No full textAtti del Convegno Nonlinear Analysis and Calculus of Variations, Perugia, 199
An inequality concerning rearrangements of functions and Hamilton-Jacobi equations
No full textWe prove an inequality concerning the decreasing rearrangement of functions. The inequality also provides a comparison result between the viscosity solution of a Cauchy problem for a Hamilton-Jacobi equation and the viscosity solution of a symmetrized proble
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