Sobolev regularity solutions for a class of singular quasilinear ODEs
Advances in Nonlinear Analysis, 2021 This paper considers an initial-boundary value problem for a class of singular quasilinear second-order ordinary differential equations with the constraint condition stemming from fluid mechanics.
Zhao Xiaofeng, Li Hengyan, Yan Weiping
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On Cauchy problem for pseudo-parabolic equation with Caputo-Fabrizio operator
Demonstratio Mathematica, 2023 In this article, we considered the pseudo-parabolic equation with Caputo-Fabrizio fractional derivative. This equation has many applications in different fields, such as science, technology, and so on.
Nghia Bui Dai +2 more
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On the local behavior of local weak solutions to some singular anisotropic elliptic equations
Advances in Nonlinear Analysis, 2022 We study the local behavior of bounded local weak solutions to a class of anisotropic singular equations of the kind ∑i=1s∂iiu+∑i=s+1N∂i(Ai(x,u,∇u))=0,x∈Ω⊂⊂RNfor1≤s≤(N−1),\mathop{\sum }\limits_{i=1}^{s}{\partial }_{ii}u+\mathop{\sum }\limits_{i=s+1}^{N}{\
Ciani Simone +2 more
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Notes on continuity result for conformable diffusion equation on the sphere: The linear case
Demonstratio Mathematica, 2022 In this article, we are interested in the linear conformable diffusion equation on the sphere. Our main goal is to establish some results on the continuity problem with respect to fractional order.
Nguyen Van Tien
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Optimality of Serrin type extension criteria to the Navier-Stokes equations
Advances in Nonlinear Analysis, 2021 We prove that a strong solution u to the Navier-Stokes equations on (0, T) can be extended if either u ∈ Lθ(0, T; U˙∞,1/θ,∞−α$\begin{array}{} \displaystyle \dot{U}^{-\alpha}_{\infty,1/\theta,\infty} \end{array}$) for 2/θ + α = 1, 0 < α < 1 or u ∈ L2(0, T;
Farwig Reinhard, Kanamaru Ryo
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The regularity of weak solutions for certain n-dimensional strongly coupled parabolic systems
Advanced Nonlinear Studies, 2022 This paper is concerned with the n-dimensional strongly coupled parabolic systems with triangular form in the cylinder Ω×(0,T]\Omega \times (0,T]. We investigate L2{L}^{2} and Hölder regularity of the derivatives of weak solutions (u1,u2)\left({u}_{1},{u}
Tan Qi-Jian
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On two-dimensional nonlocal Venttsel' problems in piecewise smooth domains [PDF]
, 2019 We establish the regularity results for solutions of nonlocal Venttsel' problems in polygonal and piecewise smooth two-dimensional ...
Creo, Simone +3 more
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The Brezis–Nirenberg problem for nonlocal systems
Advances in Nonlinear Analysis, 2016 By means of variational methods we investigate existence, nonexistence as well as regularity of weak solutions for a system of nonlocal equations involving the fractional laplacian operator and with nonlinearity reaching the critical growth and ...
Faria Luiz F. O. +4 more
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Lipschitz estimates for partial trace operators with extremal Hessian eigenvalues
Advances in Nonlinear Analysis, 2022 We consider the Dirichlet problem for partial trace operators which include the smallest and the largest eigenvalue of the Hessian matrix. It is related to two-player zero-sum differential games. No Lipschitz regularity result is known for the solutions,
Vitolo Antonio
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On some nonlinear elliptic systems with coercive perturbations in RN [PDF]
, 2003 A nonlinear elliptic system involving the p-Laplacian is considered in the whole RN: Existence of nontrivial solutions is obtained by applying critical point theory; also a regularity result is established.A nonlinear elliptic system involving the p ...
El Manouni, Said, Touzani, Abdelfattah
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