Boundary regularity for elliptic systems under a natural growth condition
نویسنده
چکیده
We consider weak solutions u ∈ u0 +W 1,2 0 (Ω,R )∩L∞(Ω,RN ) of second order nonlinear elliptic systems of the type −div a( · , u,Du) = b( · , u,Du) in Ω with an inhomogeneity obeying a natural growth condition. In dimensions n ∈ {2, 3, 4} we show that Hn−1-almost every boundary point is a regular point for Du, provided that the boundary data and the coefficients are sufficiently smooth. Mathematics Subject Classification (2000): 35J45, 35J55
منابع مشابه
Boundary regularity result for quasilinear elliptic systems
* Correspondence: shiny0320@163. com Department of Mathematics and Information Science, Zhangzhou Normal University, Zhangzhou 363000, Fujian, China Full list of author information is available at the end of the article Abstract We consider boundary regularity for weak solutions of second-order quasilinear elliptic systems under controllable growth condition, and obtain a general criterion for ...
متن کاملThe Solvability of Concave-Convex Quasilinear Elliptic Systems Involving $p$-Laplacian and Critical Sobolev Exponent
In this work, we study the existence of non-trivial multiple solutions for a class of quasilinear elliptic systems equipped with concave-convex nonlinearities and critical growth terms in bounded domains. By using the variational method, especially Nehari manifold and Palais-Smale condition, we prove the existence and multiplicity results of positive solutions.
متن کاملPartial regularity for weak solutions of nonlinear elliptic systems: the subquadratic case
We consider weak solutions of second order nonlinear elliptic systems of divergence type under subquadratic growth conditions. Via the method of A-harmonic approximation we give a characterization of regular points up to the boundary which extends known results from the quadratic and superquadratic case. The proof yields directly the optimal higher regularity on the regular set.
متن کاملBoundary Continuity of Solutions to Elliptic Equations with Nonstandard Growth
We study regularity properties of weak solutions to elliptic equations involving variable growth exponents. We prove the sufficiency of a Wiener type criterion for the regularity of boundary points. This criterion is formulated in terms of the natural capacity involving the variable growth exponent. We also prove the Hölder continuity of weak solutions up to the boundary in domains with uniform...
متن کاملA two-phase free boundary problem for a semilinear elliptic equation
In this paper we study a two-phase free boundary problem for a semilinear elliptic equation on a bounded domain $Dsubset mathbb{R}^{n}$ with smooth boundary. We give some results on the growth of solutions and characterize the free boundary points in terms of homogeneous harmonic polynomials using a fundamental result of Caffarelli and Friedman regarding the representation of functions whose ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2010