# American Institute of Mathematical Sciences

October  2015, 35(10): 4791-4804. doi: 10.3934/dcds.2015.35.4791

## Lorentz-Morrey regularity for nonlinear elliptic problems with irregular obstacles over Reifenberg flat domains

 1 Department of Mathematical Sciences and Research Institute of Mathematics, Seoul National University, Seoul 151-747, South Korea 2 School of Mathematics, Korea Institute for Advanced Study, Seoul 130-722, South Korea

Received  August 2014 Revised  February 2015 Published  April 2015

A global Calderón-Zygmund estimate type estimate in Weighted Lorentz spaces and Lorentz-Morrey spaces is obtained for weak solutions to elliptic obstacle problems of $p$-Laplacian type with discontinuous coefficients over Reifenberg flat domains.
Citation: Sun-Sig Byun, Yumi Cho. Lorentz-Morrey regularity for nonlinear elliptic problems with irregular obstacles over Reifenberg flat domains. Discrete & Continuous Dynamical Systems, 2015, 35 (10) : 4791-4804. doi: 10.3934/dcds.2015.35.4791
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##### References:
 [1] Lucas C. F. Ferreira, Jhean E. Pérez-López, Élder J. Villamizar-Roa. On the product in Besov-Lorentz-Morrey spaces and existence of solutions for the stationary Boussinesq equations. Communications on Pure & Applied Analysis, 2018, 17 (6) : 2423-2439. doi: 10.3934/cpaa.2018115 [2] Xinqun Mei, Jundong Zhou. The interior gradient estimate of prescribed Hessian quotient curvature equation in the hyperbolic space. Communications on Pure & Applied Analysis, 2021, 20 (3) : 1187-1198. doi: 10.3934/cpaa.2021012 [3] Gloria Paoli, Gianpaolo Piscitelli, Rossanno Sannipoli. A stability result for the Steklov Laplacian Eigenvalue Problem with a spherical obstacle. Communications on Pure & Applied Analysis, 2021, 20 (1) : 145-158. doi: 10.3934/cpaa.2020261 [4] Xiaomao Deng, Xiao-Chuan Cai, Jun Zou. A parallel space-time domain decomposition method for unsteady source inversion problems. Inverse Problems & Imaging, 2015, 9 (4) : 1069-1091. doi: 10.3934/ipi.2015.9.1069 [5] Alfonso Castro, Jorge Cossio, Sigifredo Herrón, Carlos Vélez. Infinitely many radial solutions for a $p$-Laplacian problem with indefinite weight. Discrete & Continuous Dynamical Systems, 2021  doi: 10.3934/dcds.2021058 [6] Guanming Gai, Yuanyuan Nie, Chunpeng Wang. A degenerate elliptic problem from subsonic-sonic flows in convergent nozzles. Communications on Pure & Applied Analysis, , () : -. doi: 10.3934/cpaa.2021070 [7] Lidan Wang, Lihe Wang, Chunqin Zhou. Classification of positive solutions for fully nonlinear elliptic equations in unbounded cylinders. Communications on Pure & Applied Analysis, 2021, 20 (3) : 1241-1261. doi: 10.3934/cpaa.2021019 [8] Tobias Breiten, Sergey Dolgov, Martin Stoll. Solving differential Riccati equations: A nonlinear space-time method using tensor trains. Numerical Algebra, Control & Optimization, 2021, 11 (3) : 407-429. doi: 10.3934/naco.2020034 [9] Emanuela R. S. Coelho, Valéria N. Domingos Cavalcanti, Vinicius A. Peralta. Exponential stability for a transmission problem of a nonlinear viscoelastic wave equation. Communications on Pure & Applied Analysis, , () : -. doi: 10.3934/cpaa.2021055 [10] Bruno Premoselli. Einstein-Lichnerowicz type singular perturbations of critical nonlinear elliptic equations in dimension 3. Discrete & Continuous Dynamical Systems, 2021  doi: 10.3934/dcds.2021069 [11] Marita Holtmannspötter, Arnd Rösch, Boris Vexler. A priori error estimates for the space-time finite element discretization of an optimal control problem governed by a coupled linear PDE-ODE system. Mathematical Control & Related Fields, 2021  doi: 10.3934/mcrf.2021014 [12] Xiaoni Chi, Zhongping Wan, Zijun Hao. A full-modified-Newton step $O(n)$ infeasible interior-point method for the special weighted linear complementarity problem. Journal of Industrial & Management Optimization, 2021  doi: 10.3934/jimo.2021082 [13] Liviana Palmisano, Bertuel Tangue Ndawa. A phase transition for circle maps with a flat spot and different critical exponents. Discrete & Continuous Dynamical Systems, 2021  doi: 10.3934/dcds.2021067 [14] Kuan-Hsiang Wang. An eigenvalue problem for nonlinear Schrödinger-Poisson system with steep potential well. Communications on Pure & Applied Analysis, , () : -. doi: 10.3934/cpaa.2021030 [15] Vaibhav Mehandiratta, Mani Mehra, Günter Leugering. Existence results and stability analysis for a nonlinear fractional boundary value problem on a circular ring with an attached edge : A study of fractional calculus on metric graph. Networks & Heterogeneous Media, 2021, 16 (2) : 155-185. doi: 10.3934/nhm.2021003 [16] Ashkan Ayough, Farbod Farhadi, Mostafa Zandieh, Parisa Rastkhadiv. Genetic algorithm for obstacle location-allocation problems with customer priorities. Journal of Industrial & Management Optimization, 2021, 17 (4) : 1753-1769. doi: 10.3934/jimo.2020044 [17] Ricardo A. Podestá, Denis E. Videla. The weight distribution of irreducible cyclic codes associated with decomposable generalized Paley graphs. Advances in Mathematics of Communications, 2021  doi: 10.3934/amc.2021002 [18] Jinyi Sun, Zunwei Fu, Yue Yin, Minghua Yang. Global existence and Gevrey regularity to the Navier-Stokes-Nernst-Planck-Poisson system in critical Besov-Morrey spaces. Discrete & Continuous Dynamical Systems - B, 2021, 26 (6) : 3409-3425. doi: 10.3934/dcdsb.2020237 [19] Simone Cacace, Maurizio Falcone. A dynamic domain decomposition for the eikonal-diffusion equation. Discrete & Continuous Dynamical Systems - S, 2016, 9 (1) : 109-123. doi: 10.3934/dcdss.2016.9.109 [20] Lei Zhang, Luming Jia. Near-field imaging for an obstacle above rough surfaces with limited aperture data. Inverse Problems & Imaging, , () : -. doi: 10.3934/ipi.2021024

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