Existence of bounded solutions for nonlinear degenerate elliptic equations in Orlicz spaces
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We prove the existence of bounded solutions for the nonlinear elliptic problem
-div α(x, u, ∇u) = ƒ in Ω,
with u ∈ W10 LM(Ω) ∩ L∞(Ω), where
α(x, s, ξ) ∙ ξ ≥ M̄-1 M(h(|s|))M(|ξ),
and h : ℝ+ →]0, 1] is a continuous monotone decreasing function with unbounded primitive. As regards the N-function M, no Δ2-condition is needed.
CitationYoussfi, A. (2007). Existence of bounded solutions for nonlinear degenerate elliptic equations in Orlicz spaces. Electronic Journal of Differential Equations, 2007(54), pp. 1-13.
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