Existence of solutions for a nonlinear elliptic equation with general flux term.

Pak, Hee Chul

Displaying similar documents to “Existence of solutions for a nonlinear elliptic equation with general flux term.”

Orlicz- Sobolev spaces and nonlinear elliptic boundary value problems

Gossez, Jean-Pierre

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Mappings of finite distortion: Compactness.

Iwaniec, Tadeusz, Koskela, Pekka, Onninen, Jani (2002)

Annales Academiae Scientiarum Fennicae. Mathematica

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Orlicz capacities and applications to some existence questions for elliptic PDEs having measure data

Alberto Fiorenza, Alain Prignet (2003)

ESAIM: Control, Optimisation and Calculus of Variations

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We study the sequence $u_{n}$ , which is solution of $- div (a (x, 𝔻 u_{n})) + Φ^{''} (| u_{n} |) u_{n} = f_{n} + g_{n}$ in $Ω$ an open bounded set of $𝐑^{N}$ and $u_{n} = 0$ on $\partial Ω$ , when $f_{n}$ tends to a measure concentrated on a set of null Orlicz-capacity. We consider the relation between this capacity and the $N$ -function $Φ$ , and prove a non-existence result.

Gradient estimates for elliptic systems in Carnot-Carathéodory spaces

Giuseppe Di Fazio, Maria Stella Fanciullo (2002)

Commentationes Mathematicae Universitatis Carolinae

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Let $X = (X_{1}, X_{2}, \dots, X_{q})$ be a system of vector fields satisfying the Hörmander condition. We prove $L_{X}^{2, λ}$ local regularity for the gradient $X u$ of a solution of the following strongly elliptic system $- X_{α}^{*} (a_{i j}^{α β} (x) X_{β} u^{j}) = g_{i} - X_{α}^{*} f_{i}^{α} (x) \forall i = 1, 2, \dots, N,$ where $a_{i j}^{α β} (x)$ are bounded functions and belong to Vanishing Mean Oscillation space.