Results 11 to 20 of about 186 (147)
A note on fractional supersolutions [PDF]
Electronic Journal of Differential Equations, 2016 We study a class of equations driven by nonlocal, possibly degenerate, integro-differential operators of differentiability order $s\in (0,1)$ and summability growth $p>1$, whose model is the fractional $p$-Laplacian with measurable coefficients.
Janne Korvenpaa +2 more
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Unbounded Supersolutions of Nonlinear Equations with Nonstandard Growth [PDF]
Boundary Value Problems, 2006 We show that every weak supersolution of a variable exponent p-Laplace equation is lower semicontinuous and that the singular set of such a function is of zero capacity if the exponent is logarithmically Hölder continuous.
Petteri Harjulehto +2 more
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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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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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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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Regularity of Supersolutions [PDF]
, 2012 The regularity for the supersolutions of the Evolutionary p-Laplace Equation is considered. In particular,the equivalence of viscosity supersolutions and p-supercaloric functions (lower semicontinuous supersolutions defined via a comparison principle) is considered.
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Singularities of positive supersolutions in elliptic PDEs [PDF]
Selecta Mathematica, 2004 Let $\\Omega\\subset\\Bbb{R}^N$ be a bounded domain and denote by ${\\rm cap}_2$ the standard $H^1$-capacity. For any Radon measure $µ$ in $\\Bbb{R}^N$, consider the \"Radon-Nikodym\" decomposition $µ=\\mu_{\\rm d}+\\mu_{\\rm c}$ with respect to ${\\rm cap}_2$, so that the diffuse measure $\\mu_{\\rm d}$ satisfies $\\mu_{\\rm d}(A)=0$ for any Borel set
Dupaigne, Louis, Ponce, Augusto
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Minimal supersolutions of convex BSDEs under constraints [PDF]
ESAIM: Probability and Statistics, 2016 We study supersolutions of a backward stochastic differential equation, the control processes of which are constrained to be continuous semimartingales of the form $dZ = Δdt + ΓdW$. The generator may depend on the decomposition $(Δ,Γ)$ and is assumed to be positive, jointly convex and lower semicontinuous, and to satisfy a superquadratic growth ...
Heyne, Gregor +3 more
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