Regularity for general functionals with double phase

被引：428

作者：

Baroni, Paolo ^{[1
]}

Colombo, Maria ^{[2
]}

Mingione, Giuseppe ^{[1
]}

机构：

[1] Univ Parma, Dipartimento SMFI, Viale Sci 53-A, I-43124 Parma, Italy

[2] ETH, Inst Theoret Studies, Clausiusstr 47, CH-8092 Zurich, Switzerland

来源：

CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS | 2018年 / 57卷 / 02期

关键词：

BOUNDARY-REGULARITY; MINIMIZERS; MINIMA; APPROXIMATION; P(X)-ENERGY; CALCULUS;

D O I：

10.1007/s00526-018-1332-z

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We prove sharp regularity results for a general class of functionals of the type w (sic) integral F (x, w, Dw) dx, featuring non-standard growth conditions and non- uniform ellipticity properties. The model case is given by the double phase integral w (sic) integral b(x, w)(vertical bar Dw vertical bar(p) + a(x)vertical bar Dw vertical bar(q))dx, 1 < p < q, a(x) >= 0, with 0 < v <= b(center dot) = L. This changes its ellipticity rate according to the geometry of the level set {a(x) = 0} of the modulating coefficient a(center dot). We also present new methods and proofs that are suitable to build regularity theorems for larger classes of non-autonomous functionals. Finally, we disclose some new interpolation type effects that, as we conjecture, should draw a general phenomenon in the setting of non-uniformly elliptic problems. Such effects naturally connect with the Lavrentiev phenomenon.

引用

页数：48

共 57 条

[1] Regularity results for electrorheological fluids: the stationary case [J].