scholarly journals Quasilinear elliptic equations with a source reaction term involving the function and its gradient and measure data

2020 ◽  
Vol 59 (5) ◽  
Author(s):  
Marie-Françoise Bidaut-Véron ◽  
Quoc-Hung Nguyen ◽  
Laurent Véron
Keyword(s):  
Elliptic Equations ◽  
Quasilinear Elliptic Equations ◽  
Measure Data ◽  
Reaction Term ◽  
Quasilinear Elliptic

scholarly journals Global W1,p(·) estimate for renormalized solutions of quasilinear equations with measure data on Reifenberg domains

2018 ◽  
Vol 7 (4) ◽  
pp. 517-533 ◽  
Author(s):  
The Anh Bui
Keyword(s):  
Elliptic Equations ◽  
Variable Exponent ◽  
Quasilinear Elliptic Equations ◽  
Measure Data ◽  
Renormalized Solutions ◽  
Lebesgue Spaces ◽  
Quasilinear Equations ◽  
Bmo Coefficients ◽  
Reifenberg Flat ◽  
Quasilinear Elliptic

AbstractIn this paper, we prove the gradient estimate for renormalized solutions to quasilinear elliptic equations with measure data on variable exponent Lebesgue spaces with BMO coefficients in a Reifenberg flat domain.

On a Class of Quasilinear Elliptic Equations with Degenerate Coerciveness and Measure Data

2018 ◽  
Vol 18 (2) ◽  
pp. 361-392 ◽  
Author(s):  
Flavia Smarrazzo
Keyword(s):  
Elliptic Equations ◽  
Quasilinear Elliptic Equations ◽  
Measure Data ◽  
Qualitative Properties ◽  
Uniqueness Results ◽  
Diffuse Part ◽  
Degenerate Elliptic ◽  
Harmonic Capacity ◽  
Quasilinear Elliptic ◽  
Standard Approximation

AbstractWe study the existence of measure-valued solutions for a class of degenerate elliptic equations with measure data. The notion of solution is natural, since it is obtained by a regularization procedure which also relies on a standard approximation of the datum μ. We provide partial uniqueness results and qualitative properties of the constructed solutions concerning, in particular, the structure of their diffuse part with respect to the harmonic-capacity.

scholarly journals Lorentz–Morrey global bounds for singular quasilinear elliptic equations with measure data

2019 ◽  
Vol 22 (05) ◽  
pp. 1950033 ◽  
Author(s):  
Minh-Phuong Tran ◽  
Thanh-Nhan Nguyen
Keyword(s):  
Elliptic Equations ◽  
Gradient Estimates ◽  
Quasilinear Elliptic Equations ◽  
Measure Data ◽  
Singular Case ◽  
Global Estimate ◽  
Quasilinear Elliptic Problem ◽  
Text Type ◽  
Local Gradient ◽  
Quasilinear Elliptic

The aim of this paper is to present the global estimate for gradient of renormalized solutions to the following quasilinear elliptic problem: [Formula: see text] in Lorentz–Morrey spaces, where [Formula: see text] ([Formula: see text]), [Formula: see text] is a finite Radon measure, [Formula: see text] is a monotone Carathéodory vector-valued function defined on [Formula: see text] and the [Formula: see text]-capacity uniform thickness condition is imposed on the complement of our domain [Formula: see text]. It is remarkable that the local gradient estimates have been proved first by Mingione in [Gradient estimates below the duality exponent, Math. Ann. 346 (2010) 571–627] at least for the case [Formula: see text], where the idea for extending such result to global ones was also proposed in the same paper. Later, the global Lorentz–Morrey and Morrey regularities were obtained by Phuc in [Morrey global bounds and quasilinear Riccati type equations below the natural exponent, J. Math. Pures Appl. 102 (2014) 99–123] for regular case [Formula: see text]. Here in this study, we particularly restrict ourselves to the singular case [Formula: see text]. The results are central to generalize our technique of good-[Formula: see text] type bounds in the previous work [M.-P. Tran, Good-[Formula: see text] type bounds of quasilinear elliptic equations for the singular case, Nonlinear Anal. 178 (2019) 266–281], where the local gradient estimates of solution to this type of equation were obtained in the Lorentz spaces. Moreover, the proofs of most results in this paper are formulated globally up to the boundary results.

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