Zobrazeno 1 - 10
of 140
pro vyhledávání: '"Ok, Jihoon"'
We study partial regularity for degenerate elliptic systems of double-phase type, where the growth function is given by $H(x,t)=t^p+a(x)t^q$ with $1
Externí odkaz:
http://arxiv.org/abs/2410.14350
We introduce fractional weighted Sobolev spaces with degenerate weights. For these spaces we provide embeddings and Poincar\'e inequalities. When the order of fractional differentiability goes to $0$ or $1$, we recover the weighted Lebesgue and Sobol
Externí odkaz:
http://arxiv.org/abs/2409.11829
We consider nonlocal equations of the type \[ (-\Delta_{p})^{s}u = \mu \quad \text{in }\Omega, \] where $\Omega \subset \mathbb{R}^{n}$ is either a bounded domain or the whole $\mathbb{R}^{n}$, $\mu$ is a Radon measure on $\Omega$, $0
Externí odkaz:
http://arxiv.org/abs/2405.11747
We obtain $L^q$-regularity estimates for weak solutions to $p$-Laplacian type equations of differential forms. In particular, we prove local Calder\'on-Zygmund type estimates for equations with discontinuous coefficients satisfying the bounded mean o
Externí odkaz:
http://arxiv.org/abs/2311.02933
Publikováno v:
Calculus of Variations and Partial Differential Equations 63 (2024), paper no. 105
We establish a partial regularity result for solutions of parabolic systems with general $\varphi$-growth, where $\varphi$ is an Orlicz function. In this setting we can develop a unified approach that is independent of the degeneracy of system and re
Externí odkaz:
http://arxiv.org/abs/2307.14779
We establish local regularity theory for parabolic systems of Uhlenbeck type with $\varphi$-growth. In particular, we prove local boundedness of weak solutions and their gradient, and then local H\"older continuity of the gradients, providing suitabl
Externí odkaz:
http://arxiv.org/abs/2302.05649
Autor:
Hästö, Peter, Ok, Jihoon
Publikováno v:
Calc. Var. Partial Differential Equations 62 (2023), article 251
We study weak solutions and minimizers $u$ of the non-autonomous problems $\operatorname{div} A(x, Du)=0$ and $\min_v \int_\Omega F(x,Dv)\,dx$ with quasi-isotropic $(p, q)$-growth. We consider the case that $u$ is bounded, H\"older continuous or lies
Externí odkaz:
http://arxiv.org/abs/2209.08917
We study generalized fractional $p$-Laplacian equations to prove local boundedness and H\"older continuity of weak solutions to such nonlocal problems by finding a suitable fractional Sobolev-Poincar\'e inquality.
Comment: 26 pages
Comment: 26 pages
Externí odkaz:
http://arxiv.org/abs/2112.13958
Autor:
Hästö, Peter, Ok, Jihoon
Publikováno v:
Arch. Ration. Mech. Anal. 245 (2022), no. 3, 1401-1436
We establish maximal local regularity results of weak solutions or local minimizers of \[ \operatorname{div} A(x, Du)=0 \quad\text{and}\quad \min_u \int_\Omega F(x,Du)\,dx, \] providing new ellipticity and continuity assumptions on $A$ or $F$ with ge
Externí odkaz:
http://arxiv.org/abs/2110.14351
Publikováno v:
In Journal of Differential Equations 15 July 2024 397:262-288
