Comparison principle and Liouville type results for singular fully nonlinear operators
Comparison principle for second order elliptic operators and applications
Comparison principles for hypersurfaces of prescribed mean curvature.
Comparison theorems for multicomponent diffusion systems: Developments since 1961.
Comparison theorems for purely non-linear parabolic differential operators
Comparison theorems for some quasilinear degenerate elliptic operators and applications to symmetry and monotonicity results
Comparison theorems for temperatures in noncylindrical domains
In questa Nota gli autori presentano alcuni risultati riguardanti il comportamento alla frontiera di domini non cilindrici delle soluzioni positive dell'equazione del calore. Una conseguenza è che due soluzioni positive qualunque, che si annullano su una parte della frontiera laterale, tendono a zero con lo stesso ordine.
Conservation laws. I: Viscosity solutions.
Conservation laws. II: Weak solutions.
Continuity Estimates for Solutions to the Prescribed-Curvature Dirichlet Problem.
Continuity of the quenching time for a parabolic equation with a nonlinear boundary condition and a potential.
Continuity of the quenching time in a heat equation with a nonlinear boundary condition.
Continuity of the quenching time in a semilinear parabolic equation
In this paper, we consider the following initial-boundary value problem [...] where Ω is a bounded domain in RN with smooth boundary ∂Ω, p > 0, Δ is the Laplacian, v is the exterior normal unit vector on ∂Ω. Under some assumptions, we show that the solution of the above problem quenches in a finite time and estimate its quenching time. We also prove the continuity of the quenching time as a function of the initial data u0. Finally, we give some numerical results to illustrate our analysis.
Continuity results for solutions of certain degenerate parabolic equations
Convergence of an entropic semi-discretization for nonlinear Fokker-Planck equations in Rd
Convergence of Rothe's method in Hölder spaces
The convergence of Rothe’s method in Hölder spaces is discussed. The obtained results are based on uniform boundedness of Rothe’s approximate solutions in Hölder spaces recently achieved by the first author. The convergence and its rate are derived inside a parabolic cylinder assuming an additional compatibility conditions.