Sulfur-crosslinkable rubber mixture comprising - a rubber blend composed of - at least one solution-polymerized diene polymer A of high molecular weight, formed from at least one conjugated diene and optionally one or more vinylaromatic compounds, having a content of vinylaromatic compound of 0% to 50% by weight, having a vinyl content of 8% to 80% by weight based on the diene content, having a glass transition temperature T g according to DSC of -100°C < T g < +20°C, having a molecular weight M w according to GPC of more than 350 000 g/mol and having a polydispersity PD of 1.1 < PD < 3 and - at least one solution-polymerized polymer B of low molecular weight, formed from at least one conjugated diene, or at least one conjugated diene and one or more vinylaromatic compounds or at least one or more than one vinylaromatic compound having a content of vinylaromatic compound of 0% to 50% by weight, having a vinyl content of 8% to 80% by weight based on any diene content present, having a glass transition temperature T g according to DSC of -100°C < T g < +80°C, having a molecular weight M w according to GPC of 1300 g/mol < M w < 10 000 g/mol and having a polydispersity PD of 1 < PD < 1.5, wherein at least one of the polymers A and B has been functionalized at the chain end and/or along the polymer chain and/or at a coupling site (multiple polymers may be attached to one functionalization site) with at least one group selected from epoxy groups, hydroxyl groups, carboxyl groups, silane sulfide groups, amino groups, siloxane groups, organosilicon groups, phthalocyanine groups and amino group-containing alkoxysilyl groups, and wherein the rubber blend is obtained by combining the polymer solutions of the polymers A and B and subsequent stripping and drying, - and as filler at least one silica and/or at least one carbon black in an amount of 25 to 300 phr, wherein the ratio of carbon black to silica in the mixture is 100:0 to 3:97. - a rubber blend composed of - at least one solution-polymerized diene polymer A of high molecular weight, formed from at least one conjugated diene and optionally one or more vinylaromatic compounds, having a content of vinylaromatic compound of 0% to 50% by weight, having a vinyl content of 8% to 80% by weight based on the diene content, having a glass transition temperature T g according to DSC of -100°C < T g < +20°C, having a molecular weight M w according to GPC of more than 350 000 g/mol and having a polydispersity PD of 1.1 < PD < 3 and - at least one solution-polymerized polymer B of low molecular weight, formed from at least one conjugated diene, or at least one conjugated diene and one or more vinylaromatic compounds or at least one or more than one vinylaromatic compound having a content of vinylaromatic compound of 0% to 50% by weight, having a vinyl content of 8% to 80% by weight based on any diene content present, having a glass transition temperature T g according to DSC of -100°C < T g < +80°C, having a molecular weight M w according to GPC of 1300 g/mol < M w < 10 000 g/mol and having a polydispersity PD of 1 < PD < 1.5, wherein at least one of the polymers A and B has been functionalized at the chain end and/or along the polymer chain and/or at a coupling site (multiple polymers may be attached to one functionalization site) with at least one group selected from epoxy groups, hydroxyl groups, carboxyl groups, silane sulfide groups, amino groups, siloxane groups, organosilicon groups, phthalocyanine groups and amino group-containing alkoxysilyl groups, and wherein the rubber blend is obtained by combining the polymer solutions of the polymers A and B and subsequent stripping and drying, or at least one conjugated diene and one or more vinylaromatic compounds or at least one or more than one vinylaromatic compound having a content of vinylaromatic compound of 0% to 50% by weight, having a vinyl content of 8% to 80% by weight based on any diene content present, having a glass transition temperature T g according to DSC of -100°C < T g < +80°C, having a molecular weight M w according to GPC of 1300 g/mol < M w < 10 000 g/mol and having a polydispersity PD of 1 < PD < 1.5, wherein at least one of the polymers A and B has been functionalized at the chain end and/or along the polymer chain and/or at a coupling site (multiple polymers may be attached to one functionalization site) with at least one group selected from epoxy groups, hydroxyl groups, carboxyl groups, silane sulfide groups, amino groups, siloxane groups, organosilicon groups, phthalocyanine groups and amino group-containing alkoxysilyl groups, and wherein the rubber blend is obtained by combining the polymer solutions of the polymers A and B and subsequent stripping and drying, - and as filler at least one silica and/or at least one carbon black in an amount of 25 to 300 phr,