Local Hölder regularity for nonlocal equations with variable powers

J Ok - Calculus of Variations and Partial Differential …, 2023 - Springer
Local Hölder regularity for nonlocal equations with variable powers | Calculus of Variations and
Partial Differential Equations Skip to main content SpringerLink Account Menu Find a journal …

Boundary regularity of mixed local-nonlocal operators and its application

A Biswas, M Modasiya, A Sen - Annali di Matematica Pura ed Applicata …, 2023 - Springer
Let Ω be a bounded C 2 domain in R n and u∈ C (R n) solves Δ u+ a I u+ C 0| D u|≥-K in Ω,
Δ u+ a I uC 0| D u|≤ K in Ω, u= 0 in Ω c, in the viscosity sense, where 0≤ a≤ A 0, C 0, K≥ 0 …

[HTML][HTML] On overdetermined problems for a general class of nonlocal operators

A Biswas, S Jarohs - Journal of Differential Equations, 2020 - Elsevier
We study the overdetermined problem for a large family of non-local operators given by
generators of subordinate Brownian motions. In particular, this family includes the fractional …

Hopf's lemma for viscosity solutions to a class of non-local equations with applications

A Biswas, J Lőrinczi - Nonlinear Analysis, 2021 - Elsevier
We consider a large family of integro-differential equations and establish a non-local
counterpart of Hopf's lemma, directly expressed in terms of the symbol of the operator. As …

Remarks on the nonlocal Dirichlet problem

T Grzywny, M Kassmann, Ł Leżaj - Potential Analysis, 2021 - Springer
We study translation-invariant integrodifferential operators that generate Lévy processes.
First, we investigate different notions of what a solution to a nonlocal Dirichlet problem is and …

Sobolev regularity theory for the non-local elliptic and parabolic equations on open sets

JH Choi, KH Kim, J Ryu - arXiv preprint arXiv:2205.11035, 2022 - arxiv.org
We study the zero exterior problem for the elliptic equation $$\Delta^{\alpha/2} u-\lambda u=
f,\quad x\in D\,;\quad u| _ {D^ c}= 0$$ as well as for the parabolic equation …

Semilinear equations for non-local operators: Beyond the fractional Laplacian

I Biočić, Z Vondraček, V Wagner - Nonlinear Analysis, 2021 - Elsevier
Semilinear equations for non-local operators: Beyond the fractional Laplacian - ScienceDirect
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Fine boundary regularity for fully nonlinear mixed local-nonlocal problems

M Modasiya, A Sen - arXiv preprint arXiv:2301.02397, 2023 - arxiv.org
We consider Dirichlet problems for fully nonlinear mixed local-nonlocal non-translation
invariant operators. For a bounded $ C^ 2$ domain $\Omega\subset\mathbb {R}^ d, $ let …

Hölder estimates for viscosity solutions of nonlocal equations with variable-order fractional Laplace term

M Yang, J Zhao, H Zhang, Y Nie - Journal of Mathematical Analysis and …, 2024 - Elsevier
We consider a class of linear integro-differential equations with variable-order fractional
Laplacian. Under sharp assumptions on the variable-order α (x, y), we prove the local …

Existence and non-existence results for a class of semilinear nonlocal operators with exterior condition

A Biswas - arXiv preprint arXiv:1805.01293, 2018 - arxiv.org
arXiv:1805.01293v1 [math.AP] 2 May 2018 Page 1 arXiv:1805.01293v1 [math.AP] 2 May 2018
EXISTENCE AND NON-EXISTENCE RESULTS FOR A CLASS OF SEMILINEAR NONLOCAL …