Isoperimetric, Sobolev, and eigenvalue inequalities via the Alexandroff-Bakelman-Pucci method: A survey
نویسندگان
چکیده
منابع مشابه
Alexandroff-Bakelman-Pucci estimate and Harnack inequality for degenerate fully non-linear elliptic equations
In this paper, we study fully non-linear elliptic equations in nondivergence form which can be degenerate when “the gradient is small”. Typical examples are either equations involving the m-Laplace operator or BellmanIsaacs equations from stochastic control problems. We establish an AlexandroffBakelman-Pucci estimate and we prove a Harnack inequality for viscosity solutions of such degenerate e...
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In this paper, we study fully non-linear elliptic equations in nondivergence form which can be degenerate or singular when “the gradient is small”. Typical examples are either equations involving the m-Laplace operator or Bellman-Isaacs equations from stochastic control problems. We establish an Alexandroff-Bakelman-Pucci estimate and we prove a Harnack inequality for viscosity solutions of suc...
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An estimate for the spectrum of the two-dimensional eigenvalue problem Am + Xe" = 0 in D (X > 0), u = 0 on 3 D is derived, and upper and lower pointwise bounds for the solutions are constructed. 1. Let D be a simply connected bounded domain in the plane with a piecewise analytic boundary 3D. Consider the nonlinear Dirichlet problem Am(x) + Xe"w = 0 in D, (1) u(x) = 0 on dD, where X is a positiv...
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ژورنال
عنوان ژورنال: Chinese Annals of Mathematics, Series B
سال: 2017
ISSN: 0252-9599,1860-6261
DOI: 10.1007/s11401-016-1067-0