1,721,022 research outputs found
Morse index and symmetry for elliptic problems with nonlinear mixed boundary conditions
Full text linkWe consider an elliptic problem of the type where Ω is a bounded Lipschitz domain in R N with a cylindrical symmetry, ν stands for the outer normal and. Under a Morse index condition, we prove cylindrical symmetry results for solutions of the above problem. As an intermediate step, we relate the Morse index of a solution of the nonlinear problem to the eigenvalues of the following linear eigenvalue problem For this one, we construct sequences of eigenvalues and provide variational characterization of them, following the usual approach for the Dirichlet case, but working in the product Hilbert space L 2 (Ω) × L 2 (Γ2)
On a class of fully nonlinear elliptic equations in dimension two
Full text linkWe study existence and asymptotic behavior of radial positive solutions of some fully nonlinear equations involving Pucci's extremal operators in dimension two. In particular we prove the existence of a positive solution of a fully nonlinear version of the Liouville equation in the plane. Moreover for the Mλ,Λ− operator, we show the existence of a critical exponent and give bounds for it
Overdetermined problems and constant mean curvature surfaces in cones
Full text linkWe consider a partially overdetermined problem in a sector-like domain Ω in a cone Σ in RN, N ≥ 2, and prove a rigidity result of Serrin type by showing that the existence of a solution implies that Ω is a spherical sector, under a convexity assumption on the cone. We also consider the related question of characterizing constant mean curvature compact surfaces Γ with boundary which satisfy a ‘gluing’ condition with respect to the cone Σ. We prove that if either the cone is convex or the surface is a radial graph then Γ must be a spherical cap. Finally we show that, under the condition that the relative boundary of the domain or the surface intersects orthogonally the cone, no other assumptions are needed
Sectional symmetry of solutions of elliptic systems in cylindrical domains
No full textIn this paper we prove a kind of rotational symmetry for solutions of semilinear elliptic systems in some bounded cylindrical domains.
The symmetry theorems obtained hold for low-Morse index solutions whenever the nonlinearities satisfy some convexity assumptions. These results extend and improve those obtained in
cite{DaPaSys, DaGlPa1, Pa, PaWe}
Sectional symmetry of solutions of elliptic systems in cylindrical domains
Full text linkIn this paper we prove a kind of rotational symmetry for solutions of semilinear elliptic systems in some bounded cylindrical domains. The symmetry theorems obtained hold for low-Morse index solutions whenever the nonlinearities satisfy some convexity assumptions. These results extend and improve those obtained in [6, 9, 16, 18]
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