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This paper deals with a mixed boundary-value problem of Ventcel type in two variables. The peculiarity of the Ventcel problem lies in the fact that one of the boundary conditions involves second order differentiation along the boundary. Under suitable assumptions on the data, we first give the definition of a weak solution, and then we prove that the problem is uniquely solvable. We also consider a particular case arising in real-world applications and discuss the resulting model.

Existence and uniqueness of classical solutions to second-order quasilinear elliptic equations.

Denny, Diane L. (2010)

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

Existence and uniqueness of entropy solutions for nonlinear elliptic equations with measure data

Lucio Boccardo, Thierry Gallouët, Luigi Orsina (1996)

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

Existence and uniqueness of Lipschitz continuous graphs with prescribed Levi curvature

Francesca Da Lio, Annamaria Montanari (2006)

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

Existence and uniqueness of solutions for a semilinear elliptic system.

Dalmasso, Robert (2005)

International Journal of Mathematics and Mathematical Sciences

Existence and uniqueness of solutions for nonlinear and non coercive problems with measure data

Pirro Oppezzo, Anna Maria Rossi (2003)

Bollettino dell'Unione Matematica Italiana

We prove the existence of a renormalized solution for a nonlinear non coercive divergence problem with lower order terms and measure data. In a particular case we also give a uniqueness result.

Existence and uniqueness of solutions for some degenerate nonlinear elliptic equations

Albo Carlos Cavalheiro (2014)

Archivum Mathematicum

In this article we are interested in the existence and uniqueness of solutions for the Dirichlet problem associated with the degenerate nonlinear elliptic equations $\begin{matrix} Δ (v (x) {| Δ u |}^{p - 2} Δ u) & - \sum_{j = 1}^{n} D_{j} [ω (x) 𝒜_{j} (x, u, \nabla u)] \\ = & f_{0} (x) - \sum_{j = 1}^{n} D_{j} f_{j} (x), i n Ω \end{matrix}$ in the setting of the weighted Sobolev spaces.

Existence and uniqueness of solutions to a semilinear elliptic system.

Chen, Zu-Chi, Cui, Ying (2009)

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

Existence and uniqueness of the solution of Laplace's equation from a model of magnetic recording.

Fleming, John L. (2008)

Applied Mathematics E-Notes [electronic only]

Existence and uniqueness of the solution of the coupled conduction-radiation energy transfer on diffuse-gray surfaces.

Qatanani, Naji, Barham, Amjad, Heeh, Qasem (2007)

Surveys in Mathematics and its Applications

Existence and uniqueness results for solutions of nonlinear equations with right hand side in $L^{1}$

A. Fiorenza, C. Sbordone (1998)

Studia Mathematica

We prove an existence and uniqueness theorem for the elliptic Dirichlet problem for the equation div a(x,∇u) = f in a planar domain Ω. Here $f \in L^{1} (Ω)$ and the solution belongs to the so-called grand Sobolev space $W_{0}^{1, 2)} (Ω)$ . This is the proper space when the right hand side is assumed to be only $L^{1}$ -integrable. In particular, we obtain the exponential integrability of the solution, which in the linear case was previously proved by Brezis-Merle and Chanillo-Li.

Existence, comportement à l'infini et stabilité dans certains problèmes quasilinéaires elliptiques et paraboliques d'ordre 2

J. P. Puel (1976)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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Displaying 281 – 300 of 504

Existence and regularity of entropy solutions for some nonlinear elliptic equations.

Existence and regularity of positive solutions for an elliptic system.

Existence and regularity of weak solutions to the Dirichletproblem for semilinear elliptic systems of higher order.

Existence and regularity of weak solutions to the prescribed mean curvature equation for a nonparametric surface.

Existence and symmetry of least energy solutions for a class of quasi-linear elliptic equations

Existence and uniqueness for a two-dimensional Ventcel problem modeling the equilibrium of a prestressed membrane