Results 11 to 20 of about 295 (155)
On the Cauchy problem for microlocally symmetrizable hyperbolic systems with log-Lipschitz coefficients [PDF]
Indiana University Mathematics Journal, 2016 The present paper concerns the well-posedness of the Cauchy problem for microlocally symmetrizable hyperbolic systems whose coefficients and symmetrizer are log-Lipschitz continuous, uniformly in time and space variables.
F. Colombini +3 more
semanticscholar +2 more sources
Dirichlet problem for quasi-linear elliptic equations
Electronic Journal of Differential Equations, 2002 We study the Dirichlet Problem associated to the quasilinear elliptic problem $$ -sum_{i=1}^{n}frac{partial }{partial x_i}mathcal{A}_i(x,u(x), abla u(x))+mathcal{B}(x,u(x),abla u(x))=0.
Azeddine Baalal, Nedra Belhaj Rhouma
doaj +1 more source
Local Hölder and maximal regularity of solutions of elliptic equations with superquadratic gradient terms [PDF]
Advances in Mathematics, 2022 We study the local Hölder regularity of strong solutions u of second-order uniformly elliptic equations having a gradient term with superquadratic growth γ > 2, and right-hand side in a Lebesgue space Lq.
Marco Cirant, G. Verzini
semanticscholar +1 more source
On the logarithmic type boundary modulus of continuity for the Stefan problem [PDF]
Advances in Mathematics, 2021 A logarithmic type modulus of continuity is established for weak solutions to a two-phase Stefan problem, up to the parabolic boundary of a cylindrical space-time domain.
Naian Liao
semanticscholar +1 more source
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
wiley +1 more source
Journal of Mathematical Inequalities, 2022 Let G = ( RN ,◦,δλ ) be a homogeneous group, Q be the homogeneous dimension of G , X0,X1, . . . ,Xm be left invariant real vector fields on G and satisfy Hörmander’s rank condition on RN . Assume that X1, . . . ,Xm (m N − 1) are homogeneous of degree one
V. Guliyev
semanticscholar +1 more source
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
doaj +1 more source
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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Nonlocal elliptic equations in bounded domains: a survey [PDF]
, 2015 In this paper we survey some results on the Dirichlet problem ( Lu = f in u = g in R n n for nonlocal operators of the form Lu(x) = PV Z Rn u(x) u(x + y) K(y)dy: We start from the very basics, proving existence of solutions, maximum principles, and ...
Xavier Ros-Oton
semanticscholar +1 more source
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
doaj +1 more source