Zobrazeno 1 - 10
of 271
pro vyhledávání: '"Urbano, Jose"'
We substantially improve in two scenarios the current state-of-the-art modulus of continuity for weak solutions to the $N$-dimensional, two-phase Stefan problem featuring a $p-$degenerate diffusion: for $p=N\geq 3$, we sharpen it to $$ \boldsymbol{\o
Externí odkaz:
http://arxiv.org/abs/2408.11555
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 a granular model for congested crowd motion and pedestrian flow. Our approach is based on an approximation through a Hele-Shaw type equation involving a degenerate operator of $p$-Laplacian type and a linear drift, for which we prove existen
Externí odkaz:
http://arxiv.org/abs/2402.17361
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
Modelling diffusion processes in heterogeneous media requires addressing inherent discontinuities across interfaces, where specific conditions are to be met. These challenges fall under the purview of Mathematical Analysis as \emph{transmission probl
Externí odkaz:
http://arxiv.org/abs/2306.15570
We prove that minimizers of the $L^{d}$-norm of the Hessian in the unit ball of $\mathbb{R}^d$ are locally of class $C^{1,\alpha}$. Our findings extend previous results on Hessian-dependent functionals to the borderline case and resonate with the H\"
Externí odkaz:
http://arxiv.org/abs/2306.10995
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 examine a transmission problem driven by a degenerate quasilinear operator with a natural interface condition. Two aspects of the problem entail genuine difficulties in the analysis: the absence of representation formulas for the operator and the
Externí odkaz:
http://arxiv.org/abs/2301.01171
Publikováno v:
J. Funct. Anal., 2024
We derive Cordes-Nirenberg type results for nonlocal elliptic integro-differential equations with deforming kernels comparable to sections of a convex solution of a Monge-Amp\`ere equation. Under a natural integrability assumption on the Monge-Amp\`e
Externí odkaz:
http://arxiv.org/abs/2212.07228
We examine Hamilton-Jacobi equations driven by fully nonlinear degenerate elliptic operators in the presence of superlinear Hamiltonians. By exploring the Ishii-Jensen inequality, we prove that viscosity solutions are locally Lipschitz-continuous, wi
Externí odkaz:
http://arxiv.org/abs/2210.15577