Study of the Regularity of Solutions for a Elasticity System with Integrable Data with Respect to the Distance Function to the Boundary
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DOI: 10.1007/s00009-018-1088-x
Abstract: In this article, we are interested in the existence, uniqueness and regularity of the solution of the linear elasticity system. More precisely, the quasi-static elasticity system. In the first part, we study the existence of… read more here.
Keywords: function; elasticity system; solution; regularity ... See more keywords
On Maximal Regularity for Abstract Parabolic Problems with Fractional Time Derivative
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DOI: 10.1007/s00009-019-1309-y
Abstract: We consider initial value problems for abstract evolution equations with fractional time derivative. Concerning the Caputo derivative $$\mathbb {D}^\alpha u$$Dαu, we show that certain assumptions, which are known to be sufficient to get a unique… read more here.
Keywords: time derivative; regularity abstract; regularity; maximal regularity ... See more keywords
On the Existence, Uniqueness and Regularity of Solutions for a Class of MHD Equations of Non-Newtonian Type
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DOI: 10.1007/s00009-020-01570-y
Abstract: In this paper, we consider a steady MHD fluid model of non-Newtonian type in a smooth bounded domain $$\Omega \in {\mathbb {R}}^3$$ . Using the iterative method, under the condition that the external force is… read more here.
Keywords: mhd; existence uniqueness; regularity; non newtonian ... See more keywords
Sobolev Regularity of Maximal Operators on Infinite Connected Graphs
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DOI: 10.1007/s00009-021-01759-9
Abstract: Let G be an infinite connected graph. We study the Sobolev regularity for the Hardy–Littlewood maximal operator and its fractional variants on G. Under certain geometric conditions on G, the endpoint Sobolev regularity properties for… read more here.
Keywords: infinite connected; maximal operators; sobolev regularity; regularity ... See more keywords
Regularity Criteria for the Axisymmetric Navier–Stokes System with Negative Weights
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DOI: 10.1007/s00025-019-1059-y
Abstract: As is well-known, for the axisymmetric Navier–Stokes equations, $$ru^{\theta }$$ obeys a maximal principle, $$\left\| ru^{\theta }(t)\right\| _{L^\infty } \leqslant \left\| ru^{\theta }_0\right\| _{L^\infty }$$. Utilizing this fact, we can establish some more weighted regularity… read more here.
Keywords: stokes system; criteria axisymmetric; regularity criteria; regularity ... See more keywords
Higher-Order Linearization and Regularity in Nonlinear Homogenization
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DOI: 10.1007/s00205-020-01519-1
Abstract: We prove large-scale $$C^\infty $$ C ∞ regularity for solutions of nonlinear elliptic equations with random coefficients, thereby obtaining a version of the statement of Hilbert’s 19th problem in the context of homogenization. The analysis… read more here.
Keywords: order linearization; homogenization; higher order; regularity ... See more keywords
Lipschitz Bounds and Nonautonomous Integrals
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DOI: 10.1007/s00205-021-01698-5
Abstract: We provide a general approach to Lipschitz regularity of solutions for a large class of vector-valued, nonautonomous variational problems exhibiting nonuniform ellipticity. The functionals considered here range from those with unbalanced polynomial growth conditions to… read more here.
Keywords: lipschitz bounds; nonautonomous integrals; bounds nonautonomous; regularity ... See more keywords
The Gursky–Streets equations
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DOI: 10.1007/s00208-020-02021-5
Abstract: Gursky–Streets introduced a formal Riemannian metric on the space of conformal metrics in a fixed conformal class of a compact Riemannian four-manifold in the context of the $$\sigma _2$$ σ 2 -Yamabe problem. The geodesic… read more here.
Keywords: regularity; yamabe problem; uniform regularity; gursky streets ... See more keywords
Regularity of prime ideals
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DOI: 10.1007/s00209-018-2089-y
Abstract: We answer several natural questions which arise from a recent paper of McCullough and Peeva providing counterexamples to the Eisenbud–Goto Regularity Conjecture. We give counterexamples using Rees algebras, and also construct counterexamples that do not… read more here.
Keywords: prime ideals; regularity prime; regularity;
Hölder Regularity of the 2D Dual Semigeostrophic Equations via Analysis of Linearized Monge–Ampère Equations
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DOI: 10.1007/s00220-018-3125-9
Abstract: We obtain the Hölder regularity of time derivative of solutions to the dual semigeostrophic equations in two dimensions when the initial potential density is bounded away from zero and infinity. Our main tool is an… read more here.
Keywords: linearized monge; regularity; dual semigeostrophic; lder regularity ... See more keywords
Optimal Regularity for the Convex Envelope and Semiconvex Functions Related to Supersolutions of Fully Nonlinear Elliptic Equations
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DOI: 10.1007/s00220-019-03370-2
Abstract: In this paper we prove optimal regularity for the convex envelope of supersolutions to general fully nonlinear elliptic equations with unbounded coefficients. More precisely, we deal with coefficients and right hand sides (RHS) in Lq… read more here.
Keywords: regularity convex; fully nonlinear; regularity; elliptic equations ... See more keywords