Das Ausstrahlungsproblem für elliptische Differentialgleichungen in Gebieten mit unbeschränkten Rand.
Das Verhalten von Lösungen semilinearer elliptischer Systeme an Ecken eines Gebietes.
De Giorgi’s Theorem, for a Class of Strongly Degenerate Elliptic Equations
In questa Nota enunciamo, per una classe di equazioni ellittiche del secondo ordine «fortemente degeneri» a coefficienti misurabili, un teorema di hölderianità delle soluzioni deboli che estende il ben noto risultato di De Giorgi e Nash. Tale risuJtato discende dalle proprietà geometriche di opportune famiglie di sfere associate agli operatori.
Decay and symmetry of positive solutions of elliptic systems in unbounded cylinders.
Decay of covariances, uniqueness of ergodic component and scaling limit for a class of systems with non-convex potential
We consider a gradient interface model on the lattice with interaction potential which is a non-convex perturbation of a convex potential. Using a technique which decouples the neighboring vertices into even and odd vertices, we show for a class of non-convex potentials: the uniqueness of ergodic component for -Gibbs measures, the decay of covariances, the scaling limit and the strict convexity of the surface tension.
Decaying Entire Positive Solutions of Quasilinear Elliptic Equations.
Decaying positive entire solutions of the -Laplacian
Decaying positive solutions of some quasilinear differential equations
The existence of decaying positive solutions in of the equations and displayed below is considered. From the existence of such solutions for the subhomogeneous cases (i.e. as ), a super-sub-solutions method (see § 2.2) enables us to obtain existence theorems for more general cases.
Decomposable systems of differential operators and generalized inverses
Defect Correction for Nonlinear Elliptic Difference Equations.
Defect correction methods for convection dominated convection-diffusion problems
Deficiency Indices of Singular Schrödinger Operators.
Deformation of domain and the limit of the variational eigenvalues of semilinear elliptic operators.
Degenerate differential operators with parameters.
Degenerate elliptic equation involving a subcritical Sobolev exponent.
Degenerate elliptic equations with measure data and nonlinear potentials
Degenerate Elliptic Operators Diagonal Systems and Variational Integrals.
Degenerate triply nonlinear problems with nonhomogeneous boundary conditions
The paper addresses the existence and uniqueness of entropy solutions for the degenerate triply nonlinear problem: b(v)t − div α(v, ▽g(v)) = f on Q:= (0, T) × Ω with the initial condition b(v(0, ·)) = b(v 0) on Ω and the nonhomogeneous boundary condition “v = u” on some part of the boundary (0, T) × ∂Ω”. The function g is continuous locally Lipschitz continuous and has a flat region [A 1, A 2,] with A 1 ≤ 0 ≤ A 2 so that the problem is of parabolic-hyperbolic type.
Degenerating Cahn-Hilliard systems coupled with mechanical effects and complete damage processes
This paper addresses analytical investigations of degenerating PDE systems for phase separation and damage processes considered on nonsmooth time-dependent domains with mixed boundary conditions for the displacement field. The evolution of the system is described by a degenerating Cahn-Hilliard equation for the concentration, a doubly nonlinear differential inclusion for the damage variable and a quasi-static balance equation for the displacement field. The analysis is performed on a time-dependent...
Degree theory for VMO maps on metric spaces
We construct a degree theory for Vanishing Mean Oscillation functions in metric spaces, following some ideas of Brezis & Nirenberg. The underlying sets of our metric spaces are bounded open subsets of and their boundaries. Then, we apply our results in order to analyze the surjectivity properties of the -harmonic extensions of VMO vector-valued functions. The operators we are dealing with are second order linear differential operators sum of squares of vector fields satisfying the hypoellipticity...