Regularity for mixed-order nonlinear fractional equations with degenerate coefficients

초록

We consider a class of nonlinear integro-differential equations whose leading operator is modeled on a superposition of (-triangle(p))(s )and (-triangle(p))(t,) where 0 < s < t < 1 < p < infinity, weighted via two possibly degenerate coefficients a(& centerdot;,& centerdot;) >= 0 and b(& centerdot;,& centerdot;) >= 0, respectively. We prove local boundedness and Holder regularity of its weak solutions under natural assumptions on the coefficients a(& centerdot;,& centerdot;), b(& centerdot;,& centerdot;) and the powers s, t, p. Moreover, when a(& centerdot;,& centerdot;) equivalent to 1, we also prove a Harnack inequality for weak solutions.

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