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Register a new userExistence of $C^alpha$ solutions to integro-PDEs
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Authors
Chenchen Mou
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This paper is concerned with existence of a $C^{alpha}$ viscosity solution of a second order non-translation invariant integro-PDE. We first obtain a weak Harnack inequality for such integro-PDE. We then use the weak Harnack inequality to prove Holder regularity and existence of solutions of the integro-PDEs.
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This paper is concerned with higher Holder regularity for viscosity solutions to non-translation invariant second order integro-PDEs, compared to cite{mou2018}. We first obtain $C^{1,alpha}$ regularity estimates for fully nonlinear integro-PDEs. We then prove the Schauder estimates for solutions if the equation is convex.
In this paper, we show $C^{2,alpha}$ interior estimates for viscosity solutions of fully non-linear, uniformly elliptic equations, which are close to linear equations and we also compute an explicit bound for the closeness.
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We establish the concept of $alpha$-dissipative solutions for the two-component Hunter-Saxton system under the assumption that either $alpha(x)=1$ or $0leq alpha(x)<1$ for all $xin mathbb{R}$. Furthermore, we investigate the Lipschitz stability of solutions with respect to time by introducing a suitable parametrized family of metrics in Lagrangian coordinates. This is necessary due to the fact that the solution space is not invariant with respect to time.
This paper introduces a convenient solution space for the uniformly elliptic fully nonlinear path dependent PDEs. It provides a wellposedness result under standard Lipschitz-type assumptions on the nonlinearity and an additional assumption formulated on some partial differential equation defined locally by freezing the path.
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