1,720,976 research outputs found
Hessian determinants as elements of dual Sobolev spaces
No full textWe present new integral formulas for the Hessian determinant. We use them for new definitions of Hessian under minimal regularity assumptions. The Hessian becomes a continuous linear functional on a Sobolev space
Regularity result for nondivergence equations with unbounded coefficients
No full textThe aim of this paper is to establish a higher integrability result for the second derivatives of solutions to nondivergence elliptic equations of the type . The matrix coefficient is assumed to belong to the space
New bounds for weights
No full textTwo new constants and are studied for weights , which are simultaneously finite exactly for weights. The special case , where is an increasing homeomorphism induces the identity . Other identities are established for such constants, when different measures are involved
A higher integrability result for nondivergence elliptic equations
No full textThe aim of this paper is to establish a higher integrability result of the second derivatives of solutions for nondivergence elliptic equations of the type . We assume that the coefficients are bounded and have small BMO-norm
New bounds for weights
No full textTwo new constants and are studied for weights , which are simultaneously finite exactly for weights. The special case , where is an increasing homeomorphism induces the identity . Other identities are established for such constants, when different measures are involved
Nondivergence elliptic equations with unbounded coefficients
No full textWe study the nonvariational equation
in domains of \reale^n. We assume that the coefficients are in and the equation is elliptic, but not uniformly, and consider in L^2(\reale^n), or even in the Zygmund class L^2\log^\alpha L(\reale^n). We also solve Dirichlet problem
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