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In this paper we provide another application of the InhomogeneousHopf-Ole\u{\i}nik Lemma (IHOL) proved in \cite{BM-IHOL-PartI} or\cite{Boyan-2}. As a matter of fact, we also provide a new and simpler proof ofa slightly weaker version IHOL for the uniformly elliptic fully nonlinear casewhich is sufficient for most purposes. The paper has essentially two parts. Inthe first part, we use IHOL for unbounded RHS to develop a Caffarelli's"Lipschitz implies $C^{1,\alpha}$" approach to prove Ladyzhenskaya-Uraltsevaboundary gradient type estimates for functions in $S^{*}(\gamma, f)$ thatvanishes on the boundary. Here, unbounded RHS means that $f\in L^{q}$ with$q>n$. This extends the celebrated Krylov's boundary gradient estimate provedin \cite{Krylov}. A Phragm\'en-Lindel\"of classification result for solutionsin half spaces is recovered from these estimates. Moreover, a H\"older estimateup to the boundary (in the half-ball) for $u(x)/x_{n}$ is obtained. In thesecond part, we extend the previous results for functions in $S^{*}(\gamma,\sigma, f)$ where $\gamma,f\in L^{q}$ with $q>n$ that have a $C^{1,Dini}$boundary data on a $W^{2,q}$ domain. Here, we use an "improvement of flatness"strategy suited to the unbounded coefficients scenario. As a consequence ofthat, a quantitative version of IHOL under pointwise $C^{1,Dini}$ boundaryregularity is obtained.

Inhomogeneous Hopf-Ole\u{i}nik Lemma and Applications. Part IV: Sharp  Krylov Boundary Gradient Type Estimates for Solutions to Fully Nonlinear  Differential Inequalities with unbounded coefficients and $C^{1,Dini}$  boundary data