On uniqueness of a solution of  with given trace.

Kuznetsov, S.E.

Displaying similar documents to “On uniqueness of a solution of $L u = u^{α}$ with given trace.”

Generalized boundary value problems for nonlinear elliptic equations.

Véron, Laurent (2001)

Electronic Journal of Differential Equations (EJDE) [electronic only]

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Boundary trace of solutions of semilinear elliptic equalities and inequalities

Laurent Véron (2004)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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The boundary trace problem for positive solutions of $- △ u + g (x, u) \geq 0$ is considered for nonlinearities of absorption type, and three different methods for defining the trace are compared. The boundary trace is obtained as a generalized Borel measure. The associated Dirichlet problem with boundary data in the set of such Borel measures is studied.

Boundary trace of positive solutions of nonlinear elliptic inequalities

Moshe Marcus, Laurent Véron (2004)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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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...

Choquet theory in metric spaces.

Okon, T. (2000)

Zeitschrift für Analysis und ihre Anwendungen

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An extended generator and Schrödinger equations.

Getoor, R.K. (1999)

Electronic Journal of Probability [electronic only]

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Strict inequality for phase transition between ferromagnetic and frustrated systems.

De Santis, Emilio (2001)

Electronic Journal of Probability [electronic only]

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Local existence of the solution to the initial-boundary value problem in nonlinear thermodiffusion in micropolar medium.

Gawinecki, J. (2000)

Zeitschrift für Analysis und ihre Anwendungen

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Finitely polynomially determined Lévy processes.

Sengupta, Arindam, Sarkar, Anish (2001)

Electronic Journal of Probability [electronic only]

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Linear stochastic parabolic equations, degenerating on the boundary of a domain.

Lototsky, Sergey V. (2001)

Electronic Journal of Probability [electronic only]

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Uniqueness of renormalized solutions to nonlinear elliptic equations with a lower order term and right-hand side in $L^{1} (Ω)$

M. F. Betta, A. Mercaldo, F. Murat, M. M. Porzio (2002)

ESAIM: Control, Optimisation and Calculus of Variations

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In this paper we prove uniqueness results for the renormalized solution, if it exists, of a class of non coercive nonlinear problems whose prototype is $\{\begin{matrix} - div (a (x) (1 + {| \nabla u |}^{2})^{\frac{p - 2}{2}} {\nabla u) + b (x) (1 + | \nabla u |}^{2})^{\frac{λ}{2}} = f & in Ω, \\ u = 0 & on \partial Ω, \end{matrix}$ where $Ω$ is a bounded open subset of $ℝ^{N}$ , $N \geq 2$ , $2 - 1 / N < p < N$ , $a$ belongs to $L^{\infty} (Ω)$ , $a (x) \geq α_{0} > 0$ , $f$ is a function in $L^{1} (Ω)$ , $b$ is a function in $L^{r} (Ω)$ and $0 \leq λ < λ^{*} (N, p, r),$ for some $r$ and $λ^{*} (N, p, r)$ .

Displaying similar documents to “On uniqueness of a solution of L u = u α with given trace.”

Displaying similar documents to “On uniqueness of a solution of $L u = u^{α}$ with given trace.”