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Optimal regularity and exponential stability for the Blackstock–Crighton equation in L p -spaces with Dirichlet and Neumann boundary conditions
The Blackstock–Crighton equation models nonlinear acoustic wave propagation in monatomic gases. In the present work, we investigate the associated...
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Local Solvability of a Linear System with a Fractional Derivative in Time in a Boundary Condition
In this paper we analyze a linear system for the Poisson equation with a boundary condition comprising the fractional derivative in time and the...
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Microlocal Regularity of Besov Type for Solutions to Quasi-elliptic Nonlinear Partial Differential Equations
Using a standard linearization technique and previously obtained microlocal properties for pseudodifferential operators with smooth coefficients, the...
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Regularity for Fully Nonlinear Equations Driven by Spatial-Inhomogeneous Nonlocal Operators
We consider a class of nonlocal operators that are not necessarily spatially homogeneous and impose mild assumptions on its kernel near zero....
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Regularity for Fully Nonlinear Integro-differential Operators with Regularly Varying Kernels
In this paper, the regularity results for the integro-differential operators of the fractional Laplacian type by Caffarelli and Silvestre (Comm. Pure...
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Maximal Regularity in Interpolation Spaces for Second-order Cauchy Problems
We study maximal regularity in interpolation spaces for the sum of three closed linear operators on a Banach space, and we apply the abstract results...
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Gelfand–Shilov Spaces: Structural Properties and Applications to Pseudodifferential Operators in ℝ n
We present the basic definitions and properties of Gelfand–Shilov spaces and discuss applications to the study of the global analytic-Gevrey...
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Removable singularities of quasilinear parabolic equations with coefficients from Kato-type classes
We establish the best possible condition for point singularities to be removable for nonlinear parabolic equations in divergent form with lower-order...
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Optimal Constant for a Smoothing Estimate of Critical Index
We generalise a result by Hoshiro [3] which considered a critical case of Kato–Yajima’s smoothing estimate...
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On the sectoriality of a class of degenerate elliptic operators arising in population genetics
We study the sectoriality of a class of degenerate second-order elliptic differential operators in the space of continuous functions on the canonical...
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On a multidimensional moving boundary problem governed by anomalous diffusion: analytical and numerical study
We study the anomalous diffusion version of the quasistationary Stefan problem (the fractional quasistationary Stefan problem) in the...
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A Note on Complete Hyperbolic Operators with log-Zygmund Coefficients
The present paper is the continuation of the recent work [7], and it is devoted to strictly hyperbolic operators with non-regular coefficients. We...
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Pointwise gradient estimates for evolution operators associated with Kolmogorov operators
We determine sufficient conditions for the occurrence of a pointwise gradient estimate for the evolution operators associated with nonautonomous...
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Boundary-value Problems for Higher-order Elliptic Equations in Non-smooth Domains
This paper presents a survey of recent results, methods, and open problems in the theory of higher-order elliptic boundary value problems on...
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Weighted L p -estimates for Elliptic Equations with Measurable Coefficients in Nonsmooth Domains
We obtain a global weighted L p estimate for the gradient of the weak solutions to divergence form elliptic equations with measurable coefficients in...
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A regularity theorem for quasilinear parabolic systems under random perturbations
Several aspects of regularity theory for parabolic systems are investigated under the effect of random perturbations. The deterministic theory, when...
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Hölder regularity for parabolic De Giorgi classes in metric measure spaces
We give a proof for the Hölder continuity of functions in the parabolic De Giorgi classes in metric measure spaces. We assume the measure to be...