Results 31 to 40 of about 1,359,151 (113)
In this work we prove that the non-negative functions belonging to suitable non-homogeneous (non-uniformly elliptic) De Giorgi classes, satisfy a weak Harnack inequality with a constant depending on the Ls-norm of the solution. Under suitable assumptions,
Henriques, Eurica +2 more
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The De Giorgi method for local and nonlocal systems
Journal of the London Mathematical Society, Volume 112, Issue 1, July 2025.Abstract We extend the De Giorgi iteration technique to the vectorial setting. For this we replace the usual scalar truncation operator by a vectorial shortening operator. As an application, we prove local boundedness for local and nonlocal nonlinear systems.
Linus Behn +3 more
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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
Electronic Journal of Differential Equations, 2017 In this article, we study some basic properties of the scale of Kato classes related with the Bessel kernel, Lorentz spaces, and Morrey spaces. Also we characterize the weak Harnack inequality for non-negative solutions of elliptic equations in terms
Rene Erlin Castillo +2 more
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Regularity and separation for Grušin‐type p‐Laplace operators
Mathematische Nachrichten, Volume 298, Issue 5, Page 1727-1757, May 2025.Abstract We analyze p‐Laplace type operators with degenerate elliptic coefficients. This investigation includes Grušin‐type p‐Laplace operators. We describe a separation phenomenon in elliptic and parabolic p‐Laplace type equations, which provide an illuminating illustration of simple jump discontinuities of the corresponding weak solutions ...
Daniel Hauer, Adam Sikora
wiley +1 more source
Another proof of the regularity of harmonic maps from a Riemannian manifold to the unit sphere
Electronic Journal of Differential Equations, 2014 We shall consider harmonic maps from $n$-dimensional compact connected Riemannian manifold with boundary to the unit sphere under the Dirichlet boundary condition. We claim that if the Dirichlet data is smooth and so-called "small", all minimizers of
Junichi Aramaki
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On the continuity of solutions to anisotropic elliptic operators in the limiting case
Bulletin of the London Mathematical Society, Volume 57, Issue 5, Page 1548-1567, May 2025.Abstract We show that local weak solutions to anisotropic elliptic equations with bounded and measurable coefficients, whose prototype is −∑i=1N∂i(|∂iu|pi−2∂iu)=0,with1
Simone Ciani +2 more
wiley +1 more source
Positive solutions for second-order boundary-value problems with phi-Laplacian
Electronic Journal of Differential Equations, 2016 This article concerns the existence, localization and multiplicity of positive solutions for the boundary-value problem $$\displaylines{ \big(\phi(u') \big) '+f(t,u) =0, \cr u(0) - a u'(0) = u'(1)= 0, }$$ where $f:[0,1]\times \mathbb{R}_{+}\to ...
Diana-Raluca Herlea
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The free boundary for semilinear problems with highly oscillating singular terms
Journal of the London Mathematical Society, Volume 111, Issue 5, May 2025.Abstract We investigate general semilinear (obstacle‐like) problems of the form Δu=f(u)$\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
Harnack inequality and no-arbitrage bounds for self-financing portfolios [PDF]
We give a direct proof of the Harnack inequality for a class of Kolmogorov operators associated with a linear SDE and we find the explicit expression of the optimal Harnack constant.
Polidoro, Sergio +2 more
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