We study weak solutions to nonlocal equations governed by integrodifferential
operators. Solutions are defined with the help of symmetric nonlocal bilinear forms.
Throughout this work, our main emphasis is on operators with general, possibly
singular, measurable kernels. We obtain regularity results which are robust with
respect to the differentiability order of the equation. Furthermore, we provide a
general tool for the derivation of Hölder a priori estimates from the weak Harnack
inequality. This tool is applicable for several local and nonlocal, linear and nonlinear
problems on metric spaces. Another aim of this work is to provide comparability
results for nonlocal quadratic forms.
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