Analysis on a Diffusive SI Epidemic Model with Logistic Source and Saturation Infection Mechanism. [PDF]
Bull Malays Math Sci Soc, 2022 Dong L, Li B, Zhang G.
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On a system involving a critically growing nonlinearity [PDF]
arXiv, 2011 This paper deals with the system \[\{{array}{ll} -\Delta u = \lambda u + q |u|^3 u \phi & \hbox{in} B_R, -\Delta \phi=q |u|^5 & \hbox{in} B_R, u=\phi=0 & \hbox{on} \partial B_R. {array}.\] We prove existence and nonexistence results depending on the value of $\lambda$.
arxiv
The Maximal Graph Dirichlet Problem in Semi-Euclidean Spaces [PDF]
arXiv, 2011 The maximal graph Dirichlet problem asks whether there exists a spacelike graph, in a semi-Euclidean space, with a given boundary and with mean curvature everywhere zero. We prove the existence of solutions to this problem under certain assumptions on the given boundary.
arxiv
A weighted $L_p$-theory for second-order elliptic and parabolic partial differential systems on a half space [PDF]
arXiv, 2012 In this paper we develop a Fefferman-Stein theorem, a Hardy-Littlewood theorem and sharp function estimations in weighted Sobolev spaces. We also provide uniqueness and existence results for second-order elliptic and parabolic partial differential systems in weighed Sobolev spaces.
arxiv
Hölder regularity of the gradient for solutions of fully nonlinear equations with sublinear first order terms [PDF]
arXiv, 2013 In this paper we shall establish some regularity results of solutions of a class of fully nonlinear equations, with a first order term which is sub-linear. We prove local H\"older regularity of the gradient both in the interior and up to the boundary.
arxiv
Elliptic and parabolic reguarity for second order divergence operators with mixed boundary conditions [PDF]
arXiv, 2013 We study second order equations and systems on non-Lipschitz domains including mixed boundary conditions. The key result is interpolation for suitable function spaces. From this, elliptic and parabolic regularity results are deduced by means of Sneiberg's isomorphism theorem.
arxiv
Shape differentiability of the eigenvalues of elliptic systems [PDF]
arXiv, 2014 We consider second order elliptic systems of partial differential equations subject to Dirichlet and Neumann boundary conditions. We prove analyticity of the elementary symmetric functions of the eigenvalues, and compute Hadamard-type formulas for such functions.
arxiv
The Friedrichs extension for elliptic wedge operators of second order [PDF]
arXiv, 2015 The paper provides an explicit description of the structure of the domain of the Friedrichs extension of a second order semibounded elliptic wedge operator, initially defined on smooth functions or sections with compact support away from the boundary, under some mild assumptions on the indicial and normal families.
arxiv
Boundedness of the solutions to nonlinear systems with Morrey data [PDF]
arXiv, 2017 We consider nonlinear elliptic systems satisfying componentwise coercivity condition. The nonlinear terms have controlled growths with respect to the solution and its gradient, while the behaviour in the independent variable is governed by functions in Morrey spaces.
arxiv
On a generalized timoshenko-kirchhoff equation [PDF]
arXiv, 2017 In this paper we consider a generalized fourth order nonlinear Kirchhoff equation in a bounded domain in $\mathbb R^{N}, N\geq2$ under Navier boundary conditions and with sublinear nonlinearity. We employ a change of variable which reduces the problem to a semilinear one.
arxiv