In this article we present the existence, uniqueness, and Hölder regularity of solutions for the non-local elliptic equations of the type (Formula presented.) where (Formula presented.) Here χ(y) is a suitable indicator function, J(y)dy is a rotationally invariant Lévy measure on ℝd (Formula presented.), and a(y) is an only measurable function with positive lower and upper bounds.
- Hölder estimates
- Integro-differential equations
- Non-local elliptic equations
- Non-symmetric measurable kernels
- Subordinate Brownian motion
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