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Regularity Results for Nonlocal Evolution Venttsel’ Problems
We consider parabolic nonlocal Venttsel’ problems in polygonal and piecewise smooth two-dimensional domains and study existence, uniqueness and...
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Dynamical Behavior of SEIR-SVS Epidemic Models with Nonlinear Incidence and Vaccination
For some infectious diseases such as mumps, HBV, there is evidence showing that vaccinated individuals always lose their immunity at different rates...
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A Boundary Estimate for Degenerate Parabolic Diffusion Equations
We prove an estimate on the modulus of continuity at a boundary point of a cylindrical domain for local weak solutions to degenerate parabolic...
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Hölder regularity for bounded solutions to a class of anisotropic operators
In this note we show the Hölder regularity for bounded solutions to a class of anisotropic elliptic operators. This result is the dual of the one...
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A boundary estimate for singular parabolic diffusion equations
We prove an estimate on the modulus of continuity at a boundary point of a cylindrical domain for local weak solutions to singular parabolic...
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Regularity of Solutions to Space–Time Fractional Wave Equations: A PDE Approach
We consider an evolution equation involving the fractional powers, of order s ∈ (0, 1), of a symmetric and uniformly elliptic second order operator...
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Gradient estimates for mean curvature flow with Neumann boundary conditions
We study the mean curvature flow of graphs both with Neumann boundary conditions and transport terms. We derive boundary gradient estimates for the...
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J. L. Lions’ problem on maximal regularity
This is a survey on recent progress concerning maximal regularity of non-autonomous equations governed by time-dependent forms on a Hilbert space. It...
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Spatial Analyticity of Solutions to Keller–Segel Equation of Parabolic–Elliptic Type
In this article, spatial analyticity of solutions to Keller–Segel equation of parabolic–elliptic type with generalized dissipation is presented....
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Gradient Continuity for Nonlinear Obstacle Problems
We prove that the gradients of solutions to obstacle problems are continuous if the gradients of obstacles satisfy a Dini type continuity assumption....
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Remarks on Local Boundedness and Local Holder Continuity of Local Weak Solutions to Anisotropic p-Laplacian Type Equations
Locally bounded, local weak solutions to a special class of quasilinear, ani-sotropic, p -Laplacian type elliptic equations, are shown to be locally...
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A Harnack inequality for the quasi-minima of scalar integral functionals with general growth conditions
In this paper we proof a Harnack inequality and a regularity theorem for quasi-minima of scalar integral functionals with general growth conditions.
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Traces of Non-regular Vector Fields on Lipschitz Domains
In this note, for Lipschitz domains \( \Omega \subset \mathbb{R}^n \)...
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Maximal Regularity for Non-autonomous Equations with Measurable Dependence on Time
In this paper we study maximal L p -regularity for evolution equations with time-dependent operators A . We merely assume a measurable dependence on...