Well posedness and regularity for heat equation with the initial condition in weighted Orlicz-Slobodetskii space subordinated to Orlicz space like lambda(log lambda)(alpha) and the logarithmic weight

作者：Kalamajska Agnieszka^*; Krbec Miroslav

来源：Revista Matematica Complutense, 2015, 28(3): 677-713.

DOI：10.1007/s13163-014-0164-4

• Orlicz-Sobolev spaces
• Orlicz-Slobodetskii spaces
• Heat equation
• Evolution problems

We consider the initial-value problem u(t) = Delta(x)u(x, t), u(x, 0) = u(x), where and belongs to certain weighted Orlicz-Slobodetskii space subordinated to the logarithmic weight. We prove that under certain assumptions on Orlicz function , the solution belongs to Orlicz-Sobolev space for certain function which in general dominates . The typical representants are , where alpha > 0.

• 出版日期2015-9