Results 1 to 10 of about 524 (177)
A Sub-Supersolution Approach for Robin Boundary Value Problems with Full Gradient Dependence [PDF]
Mathematics, 2020 The paper investigates a nonlinear elliptic problem with a Robin boundary condition, which exhibits a convection term with full dependence on the solution and its gradient. A sub- supersolution approach is developed for this type of problems.
Dumitru Motreanu +2 more
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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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The existence of positive solutions for Kirchhoff-type problems via the sub-supersolution method [PDF]
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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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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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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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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Plurisubharmonic envelopes and supersolutions [PDF]
Journal of Differential Geometry, 2019 We make a systematic study of (quasi-)plurisubharmonic envelopes on compact K hler 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-Amp re equation.
Vincent Guedj +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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Optimal Sub- or Supersolutions in Reaction-Diffusion Problems
Journal of Differential Equations, 2002 The author considers the semilinear parabolic problem \[ \begin{aligned} & {{\partial u}\over{\partial t}} = \Delta u + f(u) \quad\text{in}\quad \Omega\times(0,T), \\& {{\partial u}\over{\partial n}} + g(u) = 0 \quad\text{on}\quad \partial\Omega\times(0,T), \\ & u(x,0) = u_0(x),\end{aligned}\tag \(*\) \] where \(\Omega\) is a sufficiently smooth ...
R. Sperb
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