Results 61 to 70 of about 6,453 (213)
General Existence of Solutions to Dynamic Programming Principle [PDF]
, 2013 We provide an alternative approach to the existence of solutions to dynamic programming equations arising in the discrete game-theoretic interpretations for various nonlinear partial differential equations including the infinity Laplacian, mean curvature
Liu, Qing, Schikorra, Armin
core
A new existence result for some nonlocal problems involving Orlicz spaces and its applications
Boundary Value Problems, 2022 This paper studies some quasilinear elliptic nonlocal equations involving Orlicz–Sobolev spaces. On the one hand, a new sub-supersolution theorem is proved via the pseudomonotone operator theory; on the other hand, using the obtained theorem, we present ...
Xiaohui Qiu, Baoqiang Yan
doaj +1 more source
Supersolutions, monotone iterations, and stability
Journal of Differential Equations, 1976 where f: B x R + R is a continuously differentiable function which is increasing with respect to the second variable. Problems of this type arise in many applications, in particular in physics and chemical engineering (cf. [2, 8, 17, 231 for further references). In this connection positive solutions are of particular interest.
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Least Supersolution Approach to Regularizing Free Boundary Problems [PDF]
Archive for Rational Mechanics and Analysis, 2008 In the interesting paper under review, the author studies a free boundary problem obtained as a limit for \(\varepsilon \to 0\) of the regularizing family of semilinear elliptic equations \(\Delta u = \beta_\varepsilon(u) F(\nabla u)\), where \(\beta _\varepsilon\) approximates the Dirac delta function at the origin and \(F\) is a Lipschitz continuous ...
openaire +2 more sources
On the isoperimetric Riemannian Penrose inequality
Communications on Pure and Applied Mathematics, Volume 78, Issue 5, Page 1042-1085, May 2025.Abstract We prove that the Riemannian Penrose inequality holds for asymptotically flat 3‐manifolds with nonnegative scalar curvature and connected horizon boundary, provided the optimal decay assumptions are met, which result in the ADM$\operatorname{ADM}$ mass being a well‐defined geometric invariant.
Luca Benatti +2 more
wiley +1 more source
Convergence of the weak K\"ahler-Ricci Flow on manifolds of general type
, 2019 We study the K\"ahler-Ricci flow on compact K\"ahler manifolds whose canonical bundle is big. We show that the normalized K\"ahler-Ricci flow has long time existence in the viscosity sense, is continuous in a Zariski open set, and converges to the unique
Tô, Tat Dat
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The free boundary for semilinear problems with highly oscillating singular terms
Journal of the London Mathematical Society, Volume 111, Issue 5, May 2025.Abstract We investigate general semilinear (obstacle‐like) problems of the form Δu=f(u)$\Delta u = f(u)$, where f(u)$f(u)$ has a singularity/jump at {u=0}$\lbrace u=0\rbrace$ giving rise to a free boundary. Unlike many works on such equations where f$f$ is approximately homogeneous near {u=0}$\lbrace u = 0\rbrace$, we work under assumptions allowing ...
Mark Allen +2 more
wiley +1 more source
Abstract and Applied Analysis, 2010 We investigate the blowup properties of the positive solutions for a semilinear reaction-diffusion system with nonlinear nonlocal boundary condition.
Dengming Liu, Chunlai Mu
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Interior a priori estimates for supersolutions of fully nonlinear subelliptic equations under geometric conditions [PDF]
, 2023 Alessandro Goffi
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Time‐insensitive nonlocal parabolic Harnack estimates
Proceedings of the London Mathematical Society, Volume 130, Issue 5, May 2025.Abstract We establish new Harnack estimates that defy the waiting‐time phenomenon for global solutions to nonlocal parabolic equations. Our technique allows us to consider general nonlocal operators with bounded measurable coefficients. Moreover, we show that a waiting‐time is required for the nonlocal parabolic Harnack inequality when local solutions ...
Naian Liao, Marvin Weidner
wiley +1 more source