Sulle soluzioni delle equazioni differenziali lineari ellittiche e con coefficienti analitici
Sulle soluzioni di equazioni alle derivate parziali del primo ordine in insiemi di perimetro finito con termine noto misura
Sulle soluzioni di equazioni alle derivate parziali del primo ordine in insiemi di perimetro finito
In this paper we study boundary value problems for first order partial differential equations on sets of finite perimeter in the sense of De Giorgi (see [7]). We also study a new type of boundary value problems which has been suggested by issues about the bounce problem.
Summability of power series in several variables, with applications to singular perturbation problems and partial differential equations
Summability of semicontinuous supersolutions to a quasilinear parabolic equation
We study the so-called -superparabolic functions, which are defined as lower semicontinuous supersolutions of a quasilinear parabolic equation. In the linear case, when , we have supercaloric functions and the heat equation. We show that the -superparabolic functions have a spatial Sobolev gradient and a sharp summability exponent is given.
Summability of the solutions of nonlinear elliptic equations with right hand side measures.
Summability of the solutions to nonlinear parabolic equations with measure data.
Summation of polyparametrical functional series by the method of finite hybrid integral transforms (Fourier, Bessel)
Sums of Plane Waves, and the Range of the Random Transform.
Super and subsolutions for elliptic equations on all of .
Super and ultracontractive bounds for doubly nonlinear evolution equations.
We use logarithmic Sobolev inequalities involving the p-energy functional recently derived in [15], [21] to prove Lp-Lq smoothing and decay properties, of supercontractive and ultracontractive type, for the semigroups associated to doubly nonlinear evolution equations of the form u· = Δp(um) (with m(p - 1) ≥ 1) in an arbitrary euclidean domain, homogeneous Dirichlet boundary conditions being assumed. The bound are of the form ||u(t)||q ≤ C||u0||rγ / tβ for any r ≤ q ∈ [1,+∞) and t > 0 and...
Supercomplex structures, surface soliton equations, and quasiconformal mappings
Hurwitz pairs and triples are discussed in connection with algebra, complex analysis, and field theory. The following results are obtained: (i) A field operator of Dirac type, which is called a Hurwitz operator, is introduced by use of a Hurwitz pair and its characterization is given (Theorem 1). (ii) A field equation of the elliptic Neveu-Schwarz model of superstring theory is obtained from the Hurwitz pair (⁴,³) (Theorem 2), and its counterpart connected with the Hurwitz triple is mentioned....
Superconvergence analysis of approximate boundary-flux calculations.
Superconvergence by Steklov averaging in the finite element method
The Steklov postprocessing operator for the linear finite element method is studied. Superconvergence of order 𝓞(h²) is proved for a class of second order differential equations with zero Dirichlet boundary conditions for arbitrary space dimensions. Relations to other postprocessing and averaging schemes are discussed.
Superconvergence for rectangular mixed finite elements.
Superconvergence of a stabilized approximation for the Stokes eigenvalue problem by projection method
This paper presents a superconvergence result based on projection method for stabilized finite element approximation of the Stokes eigenvalue problem. The projection method is a postprocessing procedure that constructs a new approximation by using the least squares method. The paper complements the work of Li et al. (2012), which establishes the superconvergence result of the Stokes equations by the stabilized finite element method. Moreover, numerical tests confirm the theoretical analysis.
Superconvergence of external approximation for two-point boundary problems
The superconvergence property of a certain external method for solving two point boundary value problems is established. In the case when piecewise polynomial spaces are applied, it is proved that the convergence rate of the approximate solution at the knot points can exceed the global one.
Superconvergence of finite element method for parabolic problem.
Superconvergence of mixed finite element methods for parabolic equations
Superconvergence of the gradient of finite element solutions