A minimization problem related to the principal frequency of the p-Bilaplacian with coupled Dirichlet-Neumann boundary conditions
For each fixed integer N ≥ 2 let Ω ⊂ RN be an open, bounded and convex set with smooth boundary. For each real number p ∈ (1, ∞) define M(p; Ω) = inf u∈W2,∞ C (Ω)\{0} R (exp(|∆u| p ) − 1) dx R (exp(|u| p ) − 1) dx , where W2,∞ C (Ω) := ∩1<p<∞{u ∈ W 2,p 0 (Ω) : ∆u ∈ L ∞(Ω)}. We show that if the...
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| Dokumentumtípus: | Folyóirat |
| Megjelent: |
2023
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| Sorozat: | Electronic journal of qualitative theory of differential equations
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| Kulcsszavak: | p-Bilaplace-függvény, Dirichlet-Neumann határfeltétel, Differenciálegyenlet - elliptikus parciális, Spektrálelmélet |
| Tárgyszavak: | |
| doi: | 10.14232/ejqtde.2023.1.51 |
| Online Access: | http://acta.bibl.u-szeged.hu/88794 |
| Tartalmi kivonat: | For each fixed integer N ≥ 2 let Ω ⊂ RN be an open, bounded and convex set with smooth boundary. For each real number p ∈ (1, ∞) define M(p; Ω) = inf u∈W2,∞ C (Ω)\{0} R (exp(|∆u| p ) − 1) dx R (exp(|u| p ) − 1) dx , where W2,∞ C (Ω) := ∩1<p<∞{u ∈ W 2,p 0 (Ω) : ∆u ∈ L ∞(Ω)}. We show that if the radius of the largest ball which can be inscribed in Ω is strictly larger than a constant which depends on N then M(p; Ω) vanishes while if the radius of the largest ball which can be inscribed in Ω is strictly less than 1 then M(p; Ω) is a positive real number. Moreover, in the latter case when p is large enough we can identify the value of M(p; Ω) as being the principal frequency of the p-Bilaplacian on Ω with coupled Dirichlet–Neumann boundary conditions. |
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| Terjedelem/Fizikai jellemzők: | 9 |
| ISSN: | 1417-3875 |