Results 1 to 10 of about 106 (80)
Analytic hypoellipticity of Keldysh operators
Proceedings of the London Mathematical Society, Volume 123, Issue 5, Page 498-516, November 2021., 2021 Abstract We consider Keldysh‐type operators, P=x1Dx12+a(x)Dx1+Q(x,Dx′), x=(x1,x′) with analytic coefficients, and with Q(x,Dx′) second order, principally real and elliptic in Dx′ for x near zero. We show that if Pu=f, u∈C∞, and f is analytic in a neighbourhood of 0, then u is analytic in a neighbourhood of 0.
Jeffrey Galkowski, Maciej Zworski
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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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The exterior Dirichlet problem for the homogeneous complex k-Hessian equation
Advanced Nonlinear Studies, 2023 In this article, we consider the homogeneous complex kk-Hessian equation in an exterior domain Cn⧹Ω{{\mathbb{C}}}^{n}\setminus \Omega . We prove the existence and uniqueness of the C1,1{C}^{1,1} solution by constructing approximating solutions.
Gao Zhenghuan, Ma Xinan, Zhang Dekai
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A non-smooth Brezis-Oswald uniqueness result
Open Mathematics, 2023 We classify the non-negative critical points in W01,p(Ω){W}_{0}^{1,p}\left(\Omega ) of J(v)=∫ΩH(Dv)−F(x,v)dx,J\left(v)=\mathop{\int }\limits_{\Omega }\hspace{0.15em}H\left(Dv)-F\left(x,v){\rm{d}}x, where HH is convex and positively pp-homogeneous, while ...
Mosconi Sunra
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Double-phase parabolic equations with variable growth and nonlinear sources
Advances in Nonlinear Analysis, 2022 We study the homogeneous Dirichlet problem for the parabolic equations ut−div(A(z,∣∇u∣)∇u)=F(z,u,∇u),z=(x,t)∈Ω×(0,T),{u}_{t}-{\rm{div}}\left({\mathcal{A}}\left(z,| \nabla u| )\nabla u)=F\left(z,u,\nabla u),\hspace{1.0em}z=\left(x,t)\in \Omega \times ...
Arora Rakesh, Shmarev Sergey
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Gradient estimate of a variable power for nonlinear elliptic equations with Orlicz growth
Advances in Nonlinear Analysis, 2020 In this paper, we prove a global Calderón-Zygmund type estimate in the framework of Lorentz spaces for a variable power of the gradients to the zero-Dirichlet problem of general nonlinear elliptic equations with the nonlinearities satisfying Orlicz ...
Liang Shuang, Zheng Shenzhou
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Regularity results for singular elliptic problems
Journal of Function Spaces, Volume 4, Issue 3, Page 243-259, 2006., 2006 Some local and global regularity results for solutions of linear elliptic equations in weighted spaces are proved. Here the leading coefficients are VMO functions, while the hypotheses on the other coefficients and the boundary conditions involve a suitable weight function.
Loredana Caso, Miroslav Englis
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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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