Zobrazeno 1 - 10
of 101
pro vyhledávání: '"Damião, J."'
We investigate a class of free boundary problems with oscillatory singularities within stochastic materials. Our main result yields sharp regularity estimates along the free boundary, provided the power of the singularity varies in a Dini-continuous
Externí odkaz:
http://arxiv.org/abs/2404.03060
We study analytical and geometric properties of minimizers of non-differentiable functionals epitomizing the degenerate quenching problem. Our main finding unveils finite $(n-1)-$Hausdorff measure estimates for the pertaining free boundaries. The app
Externí odkaz:
http://arxiv.org/abs/2402.11536
Publikováno v:
Int. Math. Res. Notices IMRN (2024), no. 18, 12620-12644
In this paper, we prove some splitting results for manifolds supporting a non-constant infinity harmonic function which has at most linear growth on one side. Manifolds with non-negative Ricci or sectional curvature are considered. In dimension 2, we
Externí odkaz:
http://arxiv.org/abs/2310.07877
In this work, we present a systematic approach to investigate the existence, multiplicity, and local gradient regularity of solutions for nonlocal quasilinear equations with local gradient degeneracy. Our method involves an interactive geometric argu
Externí odkaz:
http://arxiv.org/abs/2306.15452
This paper establishes sharp local regularity estimates for viscosity solutions of fully nonlinear parabolic free boundary problems with singular absorption terms. The main difficulties are due to the blow-up of the source along the free boundary and
Externí odkaz:
http://arxiv.org/abs/2303.14520
We obtain sharp local $C^{1,\alpha}$ regularity of solutions for singular obstacle problems, Euler-Lagrange equation of which is given by $$ \Delta_p u=\gamma(u-\varphi)^{\gamma-1}\,\text{ in }\,\{u>\varphi\}, $$ for $0<\gamma<1$ and $p\ge2$. At the
Externí odkaz:
http://arxiv.org/abs/2210.09413
Publikováno v:
In Journal of Functional Analysis 1 November 2024 287(9)
Under a sharp asymptotic growth condition at infinity, we prove a Liouville type theorem for the inhomogeneous porous medium equation, provided it stays universally close to the heat equation. Additionally, for the homogeneous equation, we show that
Externí odkaz:
http://arxiv.org/abs/2201.02031
Publikováno v:
In Journal of Differential Equations 25 April 2024 389:90-113
Publikováno v:
Calc. Var. 61, 132 (2022)
In this work, we study regularity properties for nonvariational singular elliptic equations ruled by the infinity Laplacian. We obtain optimal $C^{1,\alpha}$ regularity along the free boundary. We also show existence of solutions, nondegeneracy prope
Externí odkaz:
http://arxiv.org/abs/2101.05882