Results 11 to 20 of about 6,505 (230)
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 $dZ = {\Delta}dt + {\Gamma}dW$. The generator may depend on the decomposition $({\Delta},{\
Heyne, Gregor +3 more
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A note on fractional supersolutions
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 [PDF]
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.
Francesca Bianchi +3 more
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A subsolution-supersolution method for quasilinear systems
Electronic Journal of Differential Equations, 2005 Assuming that a system of quasilinear equations of gradient type admits a strict supersolution and a strict subsolution, we show that it also admits a positive solution.
Dimitrios A. Kandilakis +1 more
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The sub-supersolution method for weak solutions [PDF]
Proceedings of the American Mathematical Society, 2008 Summary: We extend the method of sub- and supersolutions in order to prove existence of \(L^1\)-solutions of the equation \(-\Delta u = f(x,u)\) in \(\Omega\), where \(f\) is a Carathéodory function. The proof is based on the Schauder's fixed point theorem.
Marcelo Montenegro, Augusto C. Ponce
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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
Louis Dupaigne, Augusto C. Ponce
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Dual representation of minimal supersolutions of convex BSDEs [PDF]
Annales de l'Institut Henri Poincaré, Probabilités et Statistiques, 2016 We give a dual representation of minimal supersolutions of BSDEs with non-bounded, but integrable terminal conditions and under weak requirements on the generator which is allowed to depend on the value process of the equation. Conversely, we show that any dynamic risk measure satisfying such a dual representation stems from a BSDE.
Samuel Drapeau +3 more
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A weak Harnack estimate for supersolutions to the porous medium equation [PDF]
Differential and Integral Equations, 2017 In this work, we prove a weak Harnack estimate for the weak supersolutions to the porous medium equation. The proof is based on a priori estimates for the supersolutions and measure theoretical arguments.
Pekka Lehtelä
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