Existence theorems for a semilinear elliptic boundary value problem

• Autorzy: Salvatore A. Marano
• Języki publikacji: EN

Abstrakty

EN

Let Ω be a bounded domain in $ℝ^n$, n ≥ 3, with a smooth boundary ∂Ω; let L be a linear, second order, elliptic operator; let f and g be two real-valued functions defined on Ω × ℝ such that f(x,z) ≤ g(x,z) for almost every x ∈ Ω and every z ∈ ℝ. In this paper we prove that, under suitable assumptions, the problem
{ f(x,u) ≤ Lu ≤ g(x,u)   in Ω,
   u = 0     on ∂Ω,
has at least one strong solution $u ∈ W^{2,p}(Ω) ∩ W^{1,p}_0(Ω). Next, we present some remarkable special cases.

Słowa kluczowe

EN

elliptic differential inclusions; semilinear elliptic equations; strong solutions

Kategorie tematyczne

• 35R70: Partial differential equations with multivalued right-hand sides
• 35J60: Nonlinear elliptic equations

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 1994-1995
• Tom: 60
• Numer: 1
• Strony: 57-67

Daty

wydano

1994

otrzymano

1993-04-05

Twórcy

autor

Salvatore A. Marano

• Dipartimento di Matematica Università di Catania Viale A. Doria 6 95125 Catania, Italy

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