Quasilinear parabolic equations with VMO coefficients
Quasilinear parabolic equations with VMO coefficients
This paper deals with the Cauchy-Dirichlet problem and with the regular oblique derivative problem for quasilinear parabolic operators with discontinuous coefficients. To be more precise, the coefficients belong to the VMO class and the right hand side has a quadratic growth with respect to the gradient. Under several restrictions uniqueness and existence theorems in appropriate Sobolev spaces are proved.
Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations, PDEs with low regular coefficients and/or low regular data, uniqueness and existence theorems, Initial-boundary value problems for second-order parabolic equations, quadratic growth with respect to the gradient, regular oblique derivative problem, Cauchy-Dirichlet problem, discontinuous coefficients
Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations, PDEs with low regular coefficients and/or low regular data, uniqueness and existence theorems, Initial-boundary value problems for second-order parabolic equations, quadratic growth with respect to the gradient, regular oblique derivative problem, Cauchy-Dirichlet problem, discontinuous coefficients
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