EUDML

We develop a new method for proving the existence of a boundary trace, in the class of Borel measures, of nonnegative solutions of $- Δ u + g (x, u) \geq 0$ in a smooth domain $Ω$ under very general assumptions on $g$ . This new definition which extends the previous notions of boundary trace is based upon a sweeping technique by solutions of Dirichlet problems with measure boundary data. We also prove a boundary pointwise blow-up estimate of any solution of such inequalities in terms of the Poisson kernel. If the nonlinearity...

An eigenvalue problem related to Hardy’s $L^{P}$ inequality

Moshe Marcus; Itai Shafrir — 2000

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

Hardy's inequalities revisited

Haïm Brezis; Moshe Marcus — 1997

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

Capacitary estimates of positive solutions of semilinear elliptic equations with absorbtion

Moshe Marcus; Laurent Véron — 2004

Journal of the European Mathematical Society

Let $Ω$ be a bounded domain of class $C^{2}$ in $ℝ$ N and let $K$ be a compact subset of $\partial Ω$ . Assume that $q \geq (N + 1) / (N - 1)$ and denote by $U_{K}$ the maximal solution of $- Δ u + u^{q} = 0$ in $Ω$ which vanishes on $\partial Ω ∖ K$ . We obtain sharp upper and lower estimates for $U_{K}$ in terms of the Bessel capacity $C_{2 / q, q^{'}}$ and prove that $U_{K}$ is $σ$ -moderate. In addition we describe the precise asymptotic behavior of $U_{K}$ at points $σ \in K$ , which depends on the “density” of $K$ at $σ$ , measured in terms of the capacity $C_{2 / q, q^{'}}$ .

The structure and limiting behavior of locally optimal minimizers

Moshe Marcus; Alexander J. Zaslavski — 2002

Annales de l'I.H.P. Analyse non linéaire

The structure of extremals of a class of second order variational problems

Moshe Marcus; Alexander J. Zaslavski — 1999

Annales de l'I.H.P. Analyse non linéaire

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On Uniqueness of Boundary Values of Solutions of a Problem Arising in Plasma Physics.

Local behaviour of singular solutions of elliptic equations

Exceptional sets with respect to Lebesgue differentiation of functions in Sobolev spaces

Radial Averaging Transformations and Generalized Capacities.

The positive radial solutions of a class of semilinear elliptic equations.

Asymptotic behaviour of solutions and their derivatives, for semilinear elliptic problems with blowup on the boundary

Boundary trace of positive solutions of nonlinear elliptic inequalities

An eigenvalue problem related to Hardy’s $L^{P}$ inequality

Hardy's inequalities revisited

Capacitary estimates of positive solutions of semilinear elliptic equations with absorbtion

The structure and limiting behavior of locally optimal minimizers

The structure of extremals of a class of second order variational problems