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
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A Weierstrass type representation for translating solitons and singular minimal surfaces [PDF]
Journal of Mathematical Analysis and Applications, 2022 In this paper we provide aWeierstrass representation formula for translating solitons and singular minimal surfaces in R. As application we study when the euclidean Gauss map has a harmonic argument and solve a general Cauchy problem in this class of ...
Antonio Mart'inez +1 more
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Curvature estimates for $p$-convex hypersurfaces of prescribed curvature [PDF]
Revista matemática iberoamericana, 2021 . In this paper, we establish curvature estimates for p -convex hypersurfaces in R n +1 of prescribed curvature with p ≥ n 2 . The existence of a star-shaped hypersurface of prescribed curvature is obtained. We also prove a type of interior C 2 estimates
Weisong Dong
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Comparison results for solutions to the anisotropic Laplacian with Robin boundary conditions [PDF]
Nonlinear Analysis, 2021 In this paper we consider PDE’s problems involving the anisotropic Laplacian operator, with Robin boundary conditions. By means of Talenti techniques, widely used in the last decades, we prove a comparison result between the solutions of the above ...
Rossano Sannipoli
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Estimate for concentration level of the Adams functional and extremals for Adams-type inequality [PDF]
Journal of Functional Analysis, 2021 This paper is mainly concerned with the existence of extremals for the Adams inequality. We first establish an upper bound for the classical Adams functional along of all concentrated sequences in the higher order Sobolev space with homogeneous Navier ...
José Francisco Alves de Oliveira +1 more
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A nonlinear elliptic problem involving the gradient on a half space [PDF]
Discrete and Continuous Dynamical Systems. Series A, 2021 We consider perturbations of the diffusive Hamilton-Jacobi equation { −∆u = (1 + g(x))|∇u| in RN+ , u = 0 on ∂RN+ , for p > 1. We prove the existence of a classical solution provided p ∈ ( 4 3 , 2) and g is bounded with uniform radial decay to zero. 2010
A. Aghajani, C. Cowan, S. Lui
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On a system of multi-component Ginzburg-Landau vortices
Advances in Nonlinear Analysis, 2023 We study the asymptotic behavior of solutions for nn-component Ginzburg-Landau equations as ε→0\varepsilon \to 0. We prove that the minimizers converge locally in any Ck{C}^{k}-norm to a solution of a system of generalized harmonic map equations.
Hadiji Rejeb, Han Jongmin, Sohn Juhee
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Combined effects in nonlinear problems arising in the study of anisotropic continuous media [PDF]
, 2016 paper Abstract We are concerned with the Lane-Emden-Fowler equation − ∆ u = λk ( x ) u q ± h ( x ) u p in Ω, subject to the Dirichlet boundary condition u = 0 on ∂ Ω, where Ω is a smooth bounded domain in R N , k and h are variable potential functions ...
V. Ruadulescu, Dušan D. Repovš
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Large Energy Bubble Solutions for Schrödinger Equation with Supercritical Growth
Advanced Nonlinear Studies, 2021 We consider the following nonlinear Schrödinger equation involving supercritical growth:
Guo Yuxia, Liu Ting
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Analysis of positive solutions to one-dimensional generalized double phase problems
Advances in Nonlinear Analysis, 2022 We study positive solutions to the one-dimensional generalized double phase problems of the form: −(a(t)φp(u′)+b(t)φq(u′))′=λh(t)f(u),t∈(0,1),u(0)=0=u(1),\left\{\begin{array}{l}-(a\left(t){\varphi }_{p}\left(u^{\prime} )+b\left(t){\varphi }_{q}\left(u ...
Son Byungjae, Sim Inbo
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