Results 11 to 20 of about 238 (179)
A note on the supersolution method for Hardy’s inequality
Revista Matemática Complutense, 2023 AbstractWe prove a characterization of Hardy’s inequality in Sobolev–Slobodeckiĭ spaces in terms of positive local weak supersolutions of the relevant Euler-Lagrange equation. This extends previous results by Ancona Kinnunen & Korte for standard Sobolev spaces. The proof is based on variational methods.
Bianchi F. +3 more
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Plurisubharmonic envelopes and supersolutions [PDF]
Journal of Differential Geometry, 2019 We make a systematic study of (quasi-)plurisubharmonic envelopes on compact Kähler manifolds, as well as on domains of $\mathbb{C}^n$, by using and extending an approximation process due to Berman [Ber13]. We show that the quasi-psh envelope of a viscosity super-solution is a pluripotential super-solution of a given complex Monge-Ampère equation.
Guedj, Vincent +2 more
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Minimal supersolutions of BSDEs with lower semicontinuous generators [PDF]
Annales de l'Institut Henri Poincaré, Probabilités et Statistiques, 2014 We study the existence and uniqueness of minimal supersolutions of backward stochastic differential equations with generators that are jointly lower semicontinuous, bounded below by an affine function of the control variable and satisfy a specific normalization property.
Heyne, Gregor +2 more
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Solutions for a nonhomogeneous p&q-Laplacian problem via variational methods and sub-supersolution technique [PDF]
Opuscula Mathematica, 2023 In this paper it is obtained, through variational methods and sub-supersolution arguments, existence and multiplicity of solutions for a nonhomogeneous problem which arise in several branches of science such as chemical reactions, biophysics and plasma ...
Leandro S. Tavares +1 more
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Asymptotic behavior of positive solutions of a semilinear Dirichlet problem in the annulus [PDF]
Opuscula Mathematica, 2015 In this paper, we establish existence and asymptotic behavior of a positive classical solution to the following semilinear boundary value problem: \[-\Delta u=q(x)u^{\sigma }\;\text{in}\;\Omega,\quad u_{|\partial\Omega}=0.\] Here \(\Omega\) is an annulus
Safa Dridi, Bilel Khamessi
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Electronic Journal of Qualitative Theory of Differential Equations, 2021 In this paper we show existence and multiplicity of positive solutions using the sub-supersolution method and Mountain Pass Theorem in a general singular system which the operator is not homogeneous neither linear.
Suellen Arruda, Rubia Nascimento
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A sub-supersolution approach for a quasilinear Kirchhoff equation [PDF]
Journal of Mathematical Physics, 2015 In this paper, we establish an existence result for a quasilinear Kirchhoff equation, via a sub- and supersolution approach, by using the Minty-Browder’s Theorem for pseudomonotone operators theory.
Alves, Claudianor O. +1 more
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The existence of positive solutions for Kirchhoff-type problems via the sub-supersolution method
Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2018 In this paper we discuss the existence of a solution between wellordered subsolution and supersolution of the Kirchhoff equation. Using the sub-supersolution method together with a Rabinowitz-type global bifurcation theory, we establish the existence of ...
Yan Baoqiang +2 more
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Sobolev gradients of viscosity supersolutions
Nonlinear Differential Equations and Applications NoDEA, 2023 We investigate which elliptic PDEs that have the property that every viscosity supersolution is $W^{1,q}_{loc}(Ω)$, $Ω\subseteq\mathbb{R}^n$. The asymptotic cone of the operator's sublevel set seems to be essential. It turns out that much can be said if we know how this cone compares to the sublevel set of a certain minimal operator associated with the
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