Borderline Lipschitz regularity for bounded minimizers of functionals with (p,q)-growth
Karthik Adimurthi, Vivek Tewary · Forum Mathematicum · 2022
Abstract We prove local Lipschitz regularity for bounded minimizers of functionals with nonstandard ( p , q ) {(p,q)} -growth with the source term in the Lorentz space L ( N , 1 ) {L(N,1)} under the restriction q < p + 1 + p min { 1 N , 2 ( p - 1 ) N p - 2 p + 2 } . q This extends the recent work by Beck and Mingione to bounded minimizers under weaker hypothesis and is sharp for some special ranges of p, q and N.