Results 11 to 20 of about 1,215 (98)
Regularity for the two‐phase singular perturbation problems
Proceedings of the London Mathematical Society, Volume 123, Issue 5, Page 433-459, November 2021., 2021 Abstract We prove that an a priori bounded mean oscillation (BMO) gradient estimate for the two‐phase singular perturbation problem implies Lipschitz regularity for the limits. This problem arises in the mathematical theory of combustion, where the reaction diffusion is modeled by the p‐Laplacian. A key tool in our approach is the weak energy identity.
Aram Karakhanyan
wiley +1 more source
Degenerate nonlinear parabolic equations with discontinuous diffusion coefficients
Journal of the London Mathematical Society, Volume 104, Issue 2, Page 688-746, September 2021., 2021 Abstract This paper is devoted to the study of some nonlinear parabolic equations with discontinuous diffusion intensities. Such problems appear naturally in physical and biological models. Our analysis is based on variational techniques and in particular on gradient flows in the space of probability measures equipped with the distance arising in the ...
Dohyun Kwon, Alpár Richárd Mészáros
wiley +1 more source
Branch points for (almost-)minimizers of two-phase free boundary problems
Forum of Mathematics, Sigma, 2023 We study the existence and structure of branch points in two-phase free boundary problems. More precisely, we construct a family of minimizers to an Alt–Caffarelli–Friedman-type functional whose free boundaries contain branch points in the strict ...
Guy David +3 more
doaj +1 more source
Functional inequalities for the heat flow on time‐dependent metric measure spaces
Journal of the London Mathematical Society, Volume 104, Issue 2, Page 926-955, September 2021., 2021 Abstract We prove that synthetic lower Ricci bounds for metric measure spaces — both in the sense of Bakry–Émery and in the sense of Lott–Sturm–Villani — can be characterized by various functional inequalities including local Poincaré inequalities, local logarithmic Sobolev inequalities, dimension independent Harnack inequality, and logarithmic Harnack
Eva Kopfer, Karl‐Theodor Sturm
wiley +1 more source
Boundary spike‐layer solutions of the singular Keller–Segel system: existence and stability
Proceedings of the London Mathematical Society, Volume 122, Issue 1, Page 42-68, January 2021., 2021 Abstract We explore the existence and nonlinear stability of boundary spike‐layer solutions of the Keller–Segel system with logarithmic singular sensitivity in the half space, where the physical zero‐flux and Dirichlet boundary conditions are prescribed.
Jose A. Carrillo +2 more
wiley +1 more source
Source term model for elasticity system with nonlinear dissipative term in a thin domain
Demonstratio Mathematica, 2022 This article establishes an asymptotic behavior for the elasticity systems with nonlinear source and dissipative terms in a three-dimensional thin domain, which generalizes some previous works.
Dilmi Mohamed +3 more
doaj +1 more source
Sign changing solutions of Poisson's equation
Proceedings of the London Mathematical Society, Volume 121, Issue 3, Page 513-536, September 2020., 2020 Abstract Let Ω be an open, possibly unbounded, set in Euclidean space Rm with boundary ∂Ω, let A be a measurable subset of Ω with measure |A| and let γ∈(0,1). We investigate whether the solution vΩ,A,γ of −Δv=γ1Ω∖A−(1−γ)1A with v=0 on ∂Ω changes sign. Bounds are obtained for |A| in terms of geometric characteristics of Ω (bottom of the spectrum of the ...
M. van den Berg, D. Bucur
wiley +1 more source
A new equivalence of Stefan's problems for the Time-Fractional-Diffusion Equation [PDF]
, 2014 A fractional Stefan problem with a boundary convective condition is solved, where the fractional derivative of order $ \alpha \in (0,1) $ is taken in the Caputo sense.
Marcus, Eduardo Santillan +1 more
core +2 more sources
On some properties of traveling water waves with vorticity [PDF]
, 2008 We prove that for a large class of vorticity functions the crests of any corresponding traveling gravity water wave of finite depth are necessarily points of maximal horizontal velocity. We also show that for waves with nonpositive vorticity the pressure
Varvaruca, Eugen
core +1 more source
Compactness estimates for minimizers of the Alt-Phillips functional of negative exponents
Advanced Nonlinear Studies, 2023 We investigate the rigidity of global minimizers u≥0u\ge 0 of the Alt-Phillips functional involving negative power potentials ∫Ω(∣∇u∣2+u−γχ{u>0})dx,γ∈(0,2),\mathop{\int }\limits_{\Omega }(| \nabla u{| }^{2}+{u}^{-\gamma }{\chi }_{\left\{u\gt 0\right\}}){\
De Silva Daniela, Savin Ovidiu
doaj +1 more source