Zobrazeno 1 - 10
of 132
pro vyhledávání: '"Pimentel, Edgard A."'
Autor:
Pimentel, Edgard A., Stolnicki, David
We study a fully nonlinear free transmission problem in the presence of general degeneracy terms. Under minimal conditions on the degeneracy of the model, we establish the existence of viscosity solutions for the associated Dirichlet problem. Once th
Externí odkaz:
http://arxiv.org/abs/2405.05406
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
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
Autor:
Moreira, Diego R., Pimentel, Edgard A.
We prove an abstract result ensuring that one-sided geometric control yields two-sided estimates for functions satisfying general conditions. Our findings resonate in the context of nonlinear elliptic problems, including supersolutions to fully nonli
Externí odkaz:
http://arxiv.org/abs/2212.06209
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
Autor:
Pimentel, Edgard A., Walker, Miguel
We examine $L^p$-viscosity solutions to fully nonlinear elliptic equations with bounded-measurable ingredients. By considering $p_0
Externí odkaz:
http://arxiv.org/abs/2209.01960
We prove that any solution of a degenerate elliptic PDE is of class $C^1$, provided the inverse of the equation's degeneracy law satisfies an integrability criterium, viz. $\sigma^{-1} \in L^1\left (\frac{1}{\lambda} {\bf d}\lambda\right )$. The proo
Externí odkaz:
http://arxiv.org/abs/2208.11016
We prove higher-order fractional Sobolev regularity for fully nonlinear, uniformly elliptic equations in the presence of unbounded source terms. More precisely, we show the existence of a universal number $0< \varepsilon <1$, depending only on ellipt
Externí odkaz:
http://arxiv.org/abs/2204.03119