# Reference Request – Fractional Laplacian Border Regularity Type Results

Let $$u$$ to be a solution of $$– Delta u = f text {in} Omega$$ with $$u = 0 text {on} partial Omega.$$ Yes $$f in L ^ 2 ( Omega)$$then $$u in H ^ 2 ( Omega) cap H ^ {1} _ {0} ( Omega)$$provided $$Omega$$ is a smooth bounded domain.

Is this type of theorem true for the equation $$(- Delta) ^ u = f text {in} Omega$$ with $$u = 0 text {in} mathbb R ^ N – Omega$$ with $$0