منابع مشابه
Dirichlet Duality and the Nonlinear Dirichlet Problem on Riemannian Manifolds
In this paper we study the Dirichlet problem for fully nonlinear secondorder equations on a riemannian manifold. As in our previous paper [HL4] we define equations via closed subsets of the 2-jet bundle where each equation has a natural dual equation. Basic existence and uniqueness theorems are established in a wide variety of settings. However, the emphasis is on starting with a constant coeff...
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(1.2) PIH : C(Sn−1) −→ C(B) ∩ C∞(Bn), such that u = PIH f solves (1.2A) ∆Hu = 0 on B, u ∣∣ Sn−1 = f. Here, ∆H is the Laplace-Beltrami operator on B, with metric tensor (1.1). We will establish further regularity on u = PIH f when f has some further smoothness on Sn−1, and estimate du(x), in the hyperbolic metric, as x → ∂B. If n = 2, then ∆Hu = 0 if and only if ∆u = 0, where ∆ = ∂ 1 +∂ 2 2 is t...
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We study the Dirichlet problem for fully nonlinear, degenerate elliptic equations of the form F.Hessu/ D 0 on a smoothly bounded domain b Rn. In our approach the equation is replaced by a subset F Sym.Rn/ of the symmetric n nmatrices with @F fF D 0g. We establish the existence and uniqueness of continuous solutions under an explicit geometric “F -convexity” assumption on the boundary @. We a...
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ژورنال
عنوان ژورنال: Michigan Mathematical Journal
سال: 1955
ISSN: 0026-2285
DOI: 10.1307/mmj/1028990037